Geometrical Optics | Physics JEE previous year questions with Solutions

Q 1 :

A scientist is observing a bacteria through a compound microscope. For better analysis and to improve its resolving power he should (Select the best option) [2023]

increase the wave length of the light
increase the refractive index of the medium between the object and objective lens
decrease the focal length of the eye piece
decrease the diameter of the objective lens

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(2)

$P = \frac{2 μ \sin θ}{1.22 λ}$

Q 2 :

A microscope is focused on an object at the bottom of a bucket. If liquid with refractive index $\frac{5}{3}$ is poured inside the bucket, then microscope have to be raised by 30 cm to focus the object again. The height of the liquid in the bucket is [2023]

75 cm
50 cm
18 cm
12 cm

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(1)

$Shift = (d - \frac{d}{μ}) = 30 cm$

$d [1 - \frac{1}{\frac{5}{3}}] = 30$

$\Rightarrow d = \frac{30 \times 5}{2} = 75 cm$

Q 3 :

In a reflecting telescope, a secondary mirror is used to: [2023]

move the eyepiece outside the telescopic tube
make chromatic aberration zero
remove spherical aberration
reduce the problem of mechanical support

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(1)

It has advantage of a large focal length in a short telescope.

Q 4 :

In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as 5.25 mm and apparent thickness of the glass slab at 5.00 mm. Travelling microscope has 20 divisions in one cm on main scale and 50 divisions on Vernier scale is equal to 49 divisions on main scale. The estimated uncertainty in the measurement of refractive index of the slab is $\frac{x}{10} \times 10^{- 3}$ , where $x$ is _______. [2023]

(41)

$u = \frac{h}{h'} = \frac{5.25}{5.00}$

$Least count = \frac{1}{20} cm - \frac{49}{50} \cdot \frac{1}{20} cm$

$= \frac{1}{50} \times \frac{1}{20} cm = 0.01 mm$

$\ln u = \ln h - \ln h'$

$\frac{d u}{u} = \frac{d h}{h} - \frac{d h'}{h'}$

$d u = [\frac{0.01}{5.25} + \frac{0.01}{5.00}] \frac{5.25}{5.00} = \frac{41}{10} \times 10^{- 3}$

Q 5 :

In a microscope the objective is having focal length $f_{o} = 2 cm$ and eye-piece is having focal length $f_{e} = 4 cm$ . The tube length is 32 cm. The magnification produced by this microscope for normal adjustment is __________. [2026]

(100)

$m = \frac{l D}{f_{0} f_{e}}$

$= \frac{32}{2} \times \frac{25}{4}$

$m = 100$

Q 6 :

In a microscope of tube length 10 cm, two convex lenses are arranged with focal lengths of 2 cm and 5 cm. Total magnification obtained with this system for normal adjustment is ${(5)}^{k}$ . The value of $k$ is ______. [2026]

3.5
4
5
2

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4

(4)

$f_{o} = 2 cm, f_{e} = 5 cm$

$ℓ = 10 cm, D = 25 cm$

$M = \frac{ℓ}{f_{o}} \cdot \frac{D}{f_{e}} = 25$

Q 7 :

A plane glass sheet is kept over various coloured pictures. The least raised picture is:

Green
Yellow
Violet
Red

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(4)

$μ = \frac{Real thickness (x)}{Apparent thickness (y)} \Rightarrow y = \frac{x}{μ},$ $\frac{y_{v}}{y_{R}} = \frac{x}{μ_{v}} \times \frac{μ_{R}}{x} = \frac{μ_{R}}{μ_{v}}$

$Since μ_{v} > μ_{R}$ $∴$ $y_{R} > y_{v}$

$Red colour has maximum apparent thickness. Hence red colour is least raised.$

Q 8 :

In a reflecting telescope, a secondary mirror is used to:

Remove spherical aberration
Reduce the problem of mechanical support
Make chromatic aberration zero
Move the eyepiece outside the telescope tube

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4

(4)

In a reflecting telescope secondary mirror turns light towards eyepiece which is outside the telescope tube

Q 9 :

Statement – I : The formula connecting $u, v$ and $f$ for a spherical mirror is valid for mirrors whose sizes are very small compared to their radii of curvature.

Statement – II : Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.

Statement I is correct and statement II are correct
Statement I is incorrect and statement II is correct
Statement I is correct and statement II is incorrect
Both statement I and statement II are incorrect

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(3)

The formula connecting $u, v$ and $f$ for a spherical mirror $\frac{1}{u} + \frac{1}{v} = \frac{1}{f}$ is valid only for mirrors of small apertures where the size of aperture is very small as compared to the radius of curvature of the mirror. Laws of mirror are valid for plane as well as large spherical surfaces. The laws of reflection are valid when ever the light is reflected.

Q 10 :

A telescope with objective diameter R is used to observe a distant star emitting light of wavelength 500 nm, at a resolution of $5 \times 10^{- 7}$ radian. The value of R is ______ cm. [2026]

61
122
244
305

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(2)

$θ = 5 \times 10^{- 7} radian$

$λ = 500 \times 10^{- 9} m$

$θ = \frac{1.22 λ}{R}$

$R = \frac{1.22 λ}{θ} = 1.22 m = 122 cm$

Q 11 :

A compound microscope is designed with two symmetric biconvex lenses. The objective lens is cut vertically, creating two identical plano-convex lenses. One of them is used in place of original objective lens. To retain same magnification keeping the object distance unchanged, the tube length has to be ______. [2026]

increased two times
increased $\frac{3}{2}$ times
decreased two times
decreased $\frac{3}{2}$ times

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(1)

$M = \frac{L}{F_{0}} \frac{D}{F_{e}}$

$\frac{1}{F_{0}} = (n - 1) (\frac{2}{R})$

$But when cut$

$\frac{1}{F_{0}'} = (n - 1) (\frac{1}{R}) = \frac{1}{2 F_{0}}$

$So, \frac{L}{F_{0}} = \frac{L'}{F_{0}'} = 2 L$

Topic Question Set

Q 1 :

A scientist is observing a bacteria through a compound microscope. For better analysis and to improve its resolving power he should (Select the best option) [2023]

Q 2 :

A microscope is focused on an object at the bottom of a bucket. If liquid with refractive index $\frac{5}{3}$ is poured inside the bucket, then microscope have to be raised by 30 cm to focus the object again. The height of the liquid in the bucket is [2023]

Q 3 :

In a reflecting telescope, a secondary mirror is used to: [2023]

Q 5 :

In a microscope the objective is having focal length $f_{o} = 2 cm$ and eye-piece is having focal length $f_{e} = 4 cm$ . The tube length is 32 cm. The magnification produced by this microscope for normal adjustment is __________. [2026]

Q 6 :

In a microscope of tube length 10 cm, two convex lenses are arranged with focal lengths of 2 cm and 5 cm. Total magnification obtained with this system for normal adjustment is ${(5)}^{k}$ . The value of $k$ is ______. [2026]

Q 7 :

A plane glass sheet is kept over various coloured pictures. The least raised picture is:

Q 8 :

In a reflecting telescope, a secondary mirror is used to:

Q 9 :

Statement – I : The formula connecting $u, v$ and $f$ for a spherical mirror is valid for mirrors whose sizes are very small compared to their radii of curvature.

Statement – II : Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.

Q 10 :

A telescope with objective diameter R is used to observe a distant star emitting light of wavelength 500 nm, at a resolution of $5 \times 10^{- 7}$ radian. The value of R is ______ cm. [2026]

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Topic Question Set

Q 1 : A scientist is observing a bacteria through a compound microscope. For better analysis and to improve its resolving power he should (Select the best option) [2023]

Q 2 : A microscope is focused on an object at the bottom of a bucket. If liquid with refractive index 53 is poured inside the bucket, then microscope have to be raised by 30 cm to focus the object again. The height of the liquid in the bucket is [2023]

Q 3 : In a reflecting telescope, a secondary mirror is used to: [2023]

Q 5 : In a microscope the objective is having focal length fo=2 cm and eye-piece is having focal length fe=4 cm. The tube length is 32 cm. The magnification produced by this microscope for normal adjustment is __________. [2026]

Q 6 : In a microscope of tube length 10 cm, two convex lenses are arranged with focal lengths of 2 cm and 5 cm. Total magnification obtained with this system for normal adjustment is (5)k. The value of k is ______. [2026]

Q 7 : A plane glass sheet is kept over various coloured pictures. The least raised picture is:

Q 8 : In a reflecting telescope, a secondary mirror is used to:

Q 9 : Statement – I : The formula connecting u,v and f for a spherical mirror is valid for mirrors whose sizes are very small compared to their radii of curvature. Statement – II : Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.

Q 10 : A telescope with objective diameter R is used to observe a distant star emitting light of wavelength 500 nm, at a resolution of 5×10-7 radian. The value of R is ______ cm. [2026]

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Q 1 :

A scientist is observing a bacteria through a compound microscope. For better analysis and to improve its resolving power he should (Select the best option) [2023]

Q 2 :

A microscope is focused on an object at the bottom of a bucket. If liquid with refractive index $\frac{5}{3}$ is poured inside the bucket, then microscope have to be raised by 30 cm to focus the object again. The height of the liquid in the bucket is [2023]

Q 3 :

In a reflecting telescope, a secondary mirror is used to: [2023]

Q 5 :

In a microscope the objective is having focal length $f_{o} = 2 cm$ and eye-piece is having focal length $f_{e} = 4 cm$ . The tube length is 32 cm. The magnification produced by this microscope for normal adjustment is __________. [2026]

Q 6 :

In a microscope of tube length 10 cm, two convex lenses are arranged with focal lengths of 2 cm and 5 cm. Total magnification obtained with this system for normal adjustment is ${(5)}^{k}$ . The value of $k$ is ______. [2026]

Q 7 :

A plane glass sheet is kept over various coloured pictures. The least raised picture is:

Q 8 :

In a reflecting telescope, a secondary mirror is used to:

Q 9 :

Statement – I : The formula connecting $u, v$ and $f$ for a spherical mirror is valid for mirrors whose sizes are very small compared to their radii of curvature.

Statement – II : Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.

Q 10 :

A telescope with objective diameter R is used to observe a distant star emitting light of wavelength 500 nm, at a resolution of $5 \times 10^{- 7}$ radian. The value of R is ______ cm. [2026]