Geometrical Optics | Physics JEE previous year questions with Solutions

Q 11 :

A convex lens of focal length 30 cm is placed in contact with a concave lens of focal length 20 cm. An object is placed at 20 cm to the left of this lens system. The distance of the image from the lens in cm is [2025]

30
45
$\frac{60}{7}$
15

1

2

3

4

(4)

Equivalent focal length,

$\frac{1}{f} = \frac{1}{f_{1}} + \frac{1}{f_{2}}$

$\frac{1}{f} = \frac{1}{30} + \frac{1}{- 20} = \frac{2 - 3}{60} = - \frac{1}{60} \Rightarrow f = - 60 cm$

Lens formula

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$

$\frac{1}{v} - \frac{1}{- 20} = \frac{1}{- 60} \Rightarrow v = - 15 cm$

Q 12 :

Light from a point source in air falls on a spherical glass surface (refractive index, $μ$ = 1.5 and radius of curvature = 50 cm). The image is formed at a distance of 200 cm from the glass surface inside the glass. The magnitude of distance of the light source from the glass surface is ________ m. [2025]

(4)

$\frac{μ_{2}}{v} - \frac{μ_{1}}{u} = \frac{μ_{2} - μ_{1}}{R}$

$\frac{1.5}{200} - \frac{1}{- x} = \frac{1.5 - 1}{50}$

$\frac{1}{x} = \frac{1}{100} - \frac{3}{400}$

$\Rightarrow x = 400 cm$ $= 4 m$

Q 13 :

When a beam of white light is allowed to pass through a convex lens parallel to principal axis, the different colours of light converge at different point on the principle axis after refraction. This is called [2023]

scattering
chromatic aberration
spherical aberration
polarisation

1

2

3

4

(2)

The phenomena is known as chromatic aberration.

Q 14 :

A person has been using spectacles of power –1.0 D for distant vision and a separate reading glass of power 2.0 D. What is the least distance of distinct vision for this person [2023]

10 cm
40 cm
30 cm
50 cm

1

2

3

4

(4)

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}, P = 2 D$

$\Rightarrow \frac{1}{f} = \frac{2}{100} {cm}^{- 1}$

$\frac{1}{v} - (- \frac{1}{25}) = \frac{2}{100}$

$\Rightarrow \frac{1}{v} = \frac{1}{50} - \frac{1}{25} \Rightarrow v = - 50 cm$

Q 15 :

As shown in the figure, a combination of a thin plano concave lens and a thin plano convex lens is used to image an object placed at infinity. The radius of curvature of both the lenses is 30 cm and refractive index of the material for both the lenses is 1.75. Both the lenses are placed at distance of 40 cm from each other. Due to the combination, the image of the object is formed at distance $x$ = ____ cm, from concave lens. [2023]

(120)

$\frac{1}{f_{1}} = (1.75 - 1) (- \frac{1}{30})$

$\Rightarrow f_{1} = - 40 cm$

$\frac{1}{f_{2}} = (1.75 - 1) (\frac{1}{30}) \Rightarrow f_{2} = 40 cm$

Image from $L_{1}$ will be virtual and on the left of $L_{1}$ at focal length 40 cm. So the object for $L_{2}$ will be 80 cm from $L_{2}$ which is $2 f$ . Final image is formed at 80 cm from $L_{2}$ on the right.

So $x = 120$

Q 16 :

A convex lens of refractive index 1.5 and focal length 18 cm in air is immersed in water. The change in focal length of the lens will be ________ cm.

(Given refractive index of water $= \frac{4}{3}$ ) [2023]

(54)

$\frac{1}{f_{H_{2} O}} = (\frac{μ_{g}}{μ_{H_{2} O}} - 1) (\frac{2}{R}) = \frac{1}{8} (\frac{2}{R}) = \frac{1}{(4 f_{air})}$

$\Rightarrow f_{H_{2} O} = 4 f_{air} = 72 cm$

$So change in focal length = 72 - 18 = 54 cm$

Q 17 :

An object is placed on the principal axis of a convex lens of focal length 10 cm as shown. A plane mirror is placed on the other side of lens at a distance of 20 cm. The image produced by the plane mirror is 5 cm inside the mirror. The distance of the object from the lens is ________cm. [2023]

(30)

$f = 10 cm$

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$

$\frac{1}{15} - \frac{1}{- u} = \frac{1}{10}$

$\Rightarrow \frac{1}{u} = \frac{1}{10} - \frac{1}{15}$

On solving we get value of $u$ as 30 cm.

Q 18 :

Two transparent media having refractive indices 1.0 and 1.5 are separated by a spherical refracting surface of radius of curvature 30 cm. The centre of curvature of surface is towards denser medium and a point object is placed on the principal axis in rarer medium at a distance of 15 cm from the pole of the surface. The distance of image from the pole of the surface is ________cm. [2023]

(30)

$\frac{μ_{2}}{v} - \frac{μ_{1}}{u} = \frac{μ_{2} - μ_{1}}{R}$

$\frac{1.5}{v} - \frac{1}{- 15} = \frac{1.5 - 1}{30} = \frac{1}{60}$

$\frac{1.5}{v} + \frac{1}{15} = \frac{1}{60}$

$\frac{1.5}{v} = \frac{1}{60} - \frac{1}{15} = \frac{- 1}{20}$

$\frac{1.5}{v} = - \frac{1}{20} \Rightarrow v = - 30 cm$

Q 19 :

A point object, 'O' is placed in front of two thin symmetrical coaxial convex lenses $L_{1}$ and $L_{2}$ with focal length 24 cm and 9 cm respectively. The distance between two lenses is 10 cm and the object is placed 6 cm away from lens $L_{1}$ as shown in the figure. The distance between the object and the image formed by the system of two lenses is __________ cm. [2023]

(34)

$From 1^{st} lens \frac{1}{v} + \frac{1}{6} = \frac{1}{24}$

$\frac{1}{v} = \frac{1}{24} - \frac{1}{6} = - \frac{1}{8} \Rightarrow v = - 8 cm$

$From 2^{nd} lens \frac{1}{v} + \frac{1}{18} = \frac{1}{9}$

$\frac{1}{v} = \frac{1}{9} - \frac{1}{18} = \frac{1}{18} \Rightarrow v = 18$

So distance between object and its image $= 6 + 10 + 18 = 34 cm$

Q 20 :

The radius of curvature of each surface of a convex lens having refractive index 1.8 is 20 cm. The lens is now immersed in a liquid of refractive index 1.5. The ratio of power of lens in air to its power in the liquid will be $x : 1$ . The value of $x$ is ____ . [2023]

(4)

$P = (1.8 - 1) (\frac{1}{20} + \frac{1}{20}) by lens maker's formula$

$P' = (\frac{1.8}{1.5} - 1) (\frac{1}{20} + \frac{1}{20})$

$Dividing \frac{P}{P'} = \frac{0.8}{1.2 - 1} = 4$

Q 21 :

Two convex lenses of focal length 20 cm each are placed coaxially with a separation of 60 cm between them. The image of the distant object formed by the combination is at ____ cm from the first lens. [2023]

(100)

$f_{1} = 20 cm, f_{2} = 20 cm$

$1st refraction in L_{1} (I_{1})$

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f} \Rightarrow \frac{1}{v} - \frac{1}{\infty} = \frac{1}{f}$ $∴$ $v = f$

$2nd refraction in L_{2}$

$I_{1} \to object, I_{2} \to image also, u = - 40 cm and f = 20 cm$

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f} \Rightarrow \frac{1}{v} - \frac{1}{(- 40)} = \frac{1}{20}$ $∴$ $v = 40 cm$

$Correct Answer is 100 .$

Q 22 :

A bi convex lens of focal length 10 cm is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after cut is ________ D. [2023]

(5)

$Let power of each part is P_{1}, then$

$P_{1} + P_{1} = P = \frac{1}{f}$

$2 P_{1} = \frac{1}{0.1} = 10$

$P_{1} = 5 D$

Q 23 :

A collimated beam of light of diameter 2 mm is propagating along x-axis. The beam is required to be expanded in a collimated beam of diameter 14 mm using a system of two convex lenses. If first lens has focal length 40 mm, then the focal length of second lens is __________ mm. [2026]

(280)

$\frac{40}{2} = \frac{f}{14}$

$\Rightarrow f = 280 mm$

Q 24 :

A thin convex lens of focal length 5 cm and a thin concave lens of focal length 4 cm are combined together (without any gap) and this combination has magnification $m_{1}$ when an object is placed 10 cm before the convex lens. Keeping the positions of the convex lens and object undisturbed, a gap of 1 cm is introduced between the lenses by moving the concave lens away, which leads to a change in magnification of the total lens system to $m_{2}$ . The value of $| \frac{m_{1}}{m_{2}} |$ is _________. [2026]

$\frac{5}{27}$
$\frac{3}{2}$
$\frac{25}{27}$
$\frac{5}{6}$

1

2

3

4

(4)

(Dropped)

Q 25 :

A parallel beam of light travelling in air (refractive index 1.0) is incident on a convex spherical glass surface of radius of curvature 50 cm. The refractive index of glass is 1.5. The rays converge to a point at a distance $x$ cm from the centre of curvature of the spherical surface. The value of $x$ is ______ cm. [2026]

(100)

$\frac{μ_{2}}{v} - \frac{μ_{1}}{u} = \frac{μ_{2} - μ_{1}}{R} \Rightarrow \frac{1.5}{v} - \frac{1}{\infty} = \frac{1.5 - 1}{50}$

$V = 150 cm$

$x \to measure from center$

$x = V - R$

$= 150 - 50 = 100 cm$

Q 26 :

A biconvex lens is formed by using two thin plano-convex lenses, as shown in the figure. The refractive index and radius of curved surfaces are also mentioned in figure. When an object is placed on the left side of lens at a distance of 30 cm from the biconvex lens, the magnification of the image will be: [2026]

−2.5
−2
+2
+2.5

1

2

3

4

(2)

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f_{net}} = \frac{1}{f_{1}} + \frac{1}{f_{2}}$

$\frac{1}{v} + \frac{1}{30} = (1.5 - 1) (\frac{1}{15} - \frac{1}{\infty}) + (1.2 - 1) (\frac{1}{\infty} + \frac{1}{12})$

$\frac{1}{v} + \frac{1}{30} = \frac{1}{30} + \frac{1}{60}$

$v = 60$

$m = \frac{v}{u} = \frac{60}{- 30} = - 2$

Q 27 :

The size of the images of an object, formed by a thin lens are equal when the object is placed at two different positions 8 cm and 24 cm from the lens. The focal length of the lens is ______ cm. [2026]

(16)

$m = \frac{f}{f + u}$

$m_{1} = - m_{2}$

$\frac{f}{f - 8} = - \frac{f}{f - 24}$

$f - 8 = 24 - f$

$2 f = 32$

$f = 16 cm$

Q 28 :

The magnitudes of power of a biconvex lens (refractive index 1.5) and that of a plano-concave lens (refractive index 1.7) are same. If the curvature of the plano-concave lens exactly matches with the curvature of the back surface of the biconvex lens, then the ratio of radii of curvature of front and back surface of the biconvex lens is ______. [2026]

5 : 12
5 : 2
12 : 5
2 : 5

1

2

3

4

(2)

$| P_{A} |$ $=$ $| P_{B} |$

$0.5 (\frac{1}{R_{1}} + \frac{1}{R_{2}}) = \frac{0.7}{R_{2}}$

$\frac{5}{R_{1}} = \frac{2}{R_{2}}$

$\frac{R_{1}}{R_{2}} = \frac{5}{2}$

Q 29 :

A convex lens of refractive index 1.5 and focal length $f = 18$ cm is immersed in water. The difference in focal lengths of the given lens when it is in water and in air is $α \times f$ . The value of $α$ is ____.

(Refractive index of water = $\frac{4}{3}$ ) [2026]

(3)

$\frac{1}{f_{air}} = (\frac{1.5 - 1}{1}) (\frac{1}{R_{1}} + \frac{1}{R_{2}})$

$\frac{1}{f_{water}} = (\frac{1.5 - \frac{4}{3}}{\frac{4}{3}}) (\frac{1}{R_{1}} + \frac{1}{R_{2}})$

$\Rightarrow \frac{f_{water}}{f_{air}} = \frac{0.5}{0.5 / 4} = 4$

$\Rightarrow f_{water} - f_{air} = 3 f$

Topic Question Set

Q 11 :

A convex lens of focal length 30 cm is placed in contact with a concave lens of focal length 20 cm. An object is placed at 20 cm to the left of this lens system. The distance of the image from the lens in cm is [2025]

Q 13 :

When a beam of white light is allowed to pass through a convex lens parallel to principal axis, the different colours of light converge at different point on the principle axis after refraction. This is called [2023]

Q 14 :

A person has been using spectacles of power –1.0 D for distant vision and a separate reading glass of power 2.0 D. What is the least distance of distinct vision for this person [2023]

Q 16 :

A convex lens of refractive index 1.5 and focal length 18 cm in air is immersed in water. The change in focal length of the lens will be ________ cm.

(Given refractive index of water $= \frac{4}{3}$ ) [2023]

Q 20 :

The radius of curvature of each surface of a convex lens having refractive index 1.8 is 20 cm. The lens is now immersed in a liquid of refractive index 1.5. The ratio of power of lens in air to its power in the liquid will be $x : 1$ . The value of $x$ is ____ . [2023]

Q 21 :

Two convex lenses of focal length 20 cm each are placed coaxially with a separation of 60 cm between them. The image of the distant object formed by the combination is at ____ cm from the first lens. [2023]

Q 22 :

A bi convex lens of focal length 10 cm is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after cut is ________ D. [2023]

Q 23 :

A collimated beam of light of diameter 2 mm is propagating along x-axis. The beam is required to be expanded in a collimated beam of diameter 14 mm using a system of two convex lenses. If first lens has focal length 40 mm, then the focal length of second lens is __________ mm. [2026]

Q 27 :

The size of the images of an object, formed by a thin lens are equal when the object is placed at two different positions 8 cm and 24 cm from the lens. The focal length of the lens is ______ cm. [2026]

Q 29 :

A convex lens of refractive index 1.5 and focal length $f = 18$ cm is immersed in water. The difference in focal lengths of the given lens when it is in water and in air is $α \times f$ . The value of $α$ is ____.

(Refractive index of water = $\frac{4}{3}$ ) [2026]

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Topic Question Set

Q 11 : A convex lens of focal length 30 cm is placed in contact with a concave lens of focal length 20 cm. An object is placed at 20 cm to the left of this lens system. The distance of the image from the lens in cm is [2025]

Q 13 : When a beam of white light is allowed to pass through a convex lens parallel to principal axis, the different colours of light converge at different point on the principle axis after refraction. This is called [2023]

Q 14 : A person has been using spectacles of power –1.0 D for distant vision and a separate reading glass of power 2.0 D. What is the least distance of distinct vision for this person [2023]

Q 16 : A convex lens of refractive index 1.5 and focal length 18 cm in air is immersed in water. The change in focal length of the lens will be ________ cm. (Given refractive index of water =43) [2023]

Q 20 : The radius of curvature of each surface of a convex lens having refractive index 1.8 is 20 cm. The lens is now immersed in a liquid of refractive index 1.5. The ratio of power of lens in air to its power in the liquid will be x:1. The value of x is ____ . [2023]

Q 21 : Two convex lenses of focal length 20 cm each are placed coaxially with a separation of 60 cm between them. The image of the distant object formed by the combination is at ____ cm from the first lens. [2023]

Q 22 : A bi convex lens of focal length 10 cm is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after cut is ________ D. [2023]

Q 23 : A collimated beam of light of diameter 2 mm is propagating along x-axis. The beam is required to be expanded in a collimated beam of diameter 14 mm using a system of two convex lenses. If first lens has focal length 40 mm, then the focal length of second lens is __________ mm. [2026]

Q 27 : The size of the images of an object, formed by a thin lens are equal when the object is placed at two different positions 8 cm and 24 cm from the lens. The focal length of the lens is ______ cm. [2026]

Q 29 : A convex lens of refractive index 1.5 and focal length f=18 cm is immersed in water. The difference in focal lengths of the given lens when it is in water and in air is α×f. The value of α is ____. (Refractive index of water = 43) [2026]

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Q 11 :

A convex lens of focal length 30 cm is placed in contact with a concave lens of focal length 20 cm. An object is placed at 20 cm to the left of this lens system. The distance of the image from the lens in cm is [2025]

Q 13 :

When a beam of white light is allowed to pass through a convex lens parallel to principal axis, the different colours of light converge at different point on the principle axis after refraction. This is called [2023]

Q 14 :

A person has been using spectacles of power –1.0 D for distant vision and a separate reading glass of power 2.0 D. What is the least distance of distinct vision for this person [2023]

Q 16 :

A convex lens of refractive index 1.5 and focal length 18 cm in air is immersed in water. The change in focal length of the lens will be ________ cm.

(Given refractive index of water $= \frac{4}{3}$ ) [2023]

Q 20 :

The radius of curvature of each surface of a convex lens having refractive index 1.8 is 20 cm. The lens is now immersed in a liquid of refractive index 1.5. The ratio of power of lens in air to its power in the liquid will be $x : 1$ . The value of $x$ is ____ . [2023]

Q 21 :

Two convex lenses of focal length 20 cm each are placed coaxially with a separation of 60 cm between them. The image of the distant object formed by the combination is at ____ cm from the first lens. [2023]

Q 22 :

A bi convex lens of focal length 10 cm is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after cut is ________ D. [2023]

Q 23 :

A collimated beam of light of diameter 2 mm is propagating along x-axis. The beam is required to be expanded in a collimated beam of diameter 14 mm using a system of two convex lenses. If first lens has focal length 40 mm, then the focal length of second lens is __________ mm. [2026]

Q 27 :

The size of the images of an object, formed by a thin lens are equal when the object is placed at two different positions 8 cm and 24 cm from the lens. The focal length of the lens is ______ cm. [2026]

Q 29 :

A convex lens of refractive index 1.5 and focal length $f = 18$ cm is immersed in water. The difference in focal lengths of the given lens when it is in water and in air is $α \times f$ . The value of $α$ is ____.

(Refractive index of water = $\frac{4}{3}$ ) [2026]