Q 41 :

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 42 :

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 43 :

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 44 :

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 $\left|\frac{m_1}{m_2}\right|$ is _________.           [2026]

• $\frac{5}{27}$

   

• $\frac{3}{2}$

   

• $\frac{25}{27}$

   

• $\frac{5}{6}$

   

Q 45 :

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]

Q 46 :

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

   

Q 47 :

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 48 :

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

   

Q 49 :

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 $\alpha \times f$. The value of $\alpha$ is ____.

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