If the focal length of the eye-piece of a telescope is doubled, its magnifying power (m) will be

• 2 m

• 3 m

• $\frac{\mathrm{m}}{2}$

• 4 m

A plano-concave lens is made of glass of refractive index 1.5 and the radius of curvature of its curved face is 100 cm. What is the power of the lens ?

• + 0.5 D

• − 0.5 D

• − 2 D

• + 2 D

If the velocity of light in vacuum is 3 x 10⁸ ms^-1, the time taken (in nanosecond) to travel through a glass plate of thickness 10 cm and refractive index 1.5 is

• 0.5

• 1.0

• 2.0

• 3.0

An object placed in front of a concave mirror at a distance of x cm from the pole gives a 3 times magnified real image. If it is moved to a distance of (x + 5) cm, the magnification of the image becomes 2. The focal length of the mirror is

• 15 cm

• 20 cm

• 25 cm

• 30 cm

A plano-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices µ₁ and µ₂ and R is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is

• $\frac{\mathrm{R}}{2\left({\mathrm{\mu }}_1 + {\mathrm{\mu }}_2\right)}$

• $\frac{\mathrm{R}}{2\left({\mathrm{\mu }}_1 - {\mathrm{\mu }}_2\right)}$

• $\frac{\mathrm{R}}{\left({\mathrm{\mu }}_1 - {\mathrm{\mu }}_2\right)}$

• $\frac{2\mathrm{R}}{\left({\mathrm{\mu }}_2 - {\mathrm{\mu }}_1\right)}$

For a normal eye, the cornea of eye provides a converging power of 40 D and the least converging power of the eye lens behind the cornea is 20 D. Using this information, the distance between the retina and the cornea-eye lens can be estimated to be

• 5 cm

• 2.5 cm

• 1.67 cm

• 1.5 cm

A luminous object is separated from a screen by distance d. A convex lens is placed between the object and the screen such that it forms a distinct image on the screen. The maximum possible focal length of this convex lens is

• 4d

• 2d

• $\frac{\mathrm{d}}{2}$

• $\frac{\mathrm{d}}{4}$

388.

The intermediate image formed by the objective of a compound microscope is

• real, inverted and magnified

• real, erect and magnified

• virtual, erect and magnified

• virtual, inverted and magnified

A glass slab consists of thin uniform layers of progressively decreasing refractive indices RI (see figure) such that the RI of any layer is µ − m Δµ. Here, µ and Δµ denote the RI of 0th layer and the difference in RI between any two consecutive layers, respectively. The integer m =0, 1, 2, 3, ... denotes the numbers of the successive layers. A ray of light from the 0th layer enters the 1st layer at an angle of incidence of 30°. After undergoing the mth refraction, the ray emerges parallel to the interface. If µ = 1.5 and Δµ = 0.015, the value of m is

• 20

• 30

• 40

• 50

An object is placed 30 cm away from a convex lens of focal length 10 cm and a sharp image is formed on a screen. Now a concave lens is placed in contact with the convex lens. The screen now has to be moved by 45 cm to get a sharp image again. The magnitude of focal length of the concave lens is (in cm)

• 72

• 60

• 36

• 20