When a biconvex lens of glass having a refractive index of 1.47 is dipped in a liquid, it acts as a plane sheet of glass. The liquid must have a refractive index:

1. equal to that of glass.

2. less than one.

3. greater than that of glass.

4. less than that of glass.

A ray of light is incident at an angle of incidence, i, on one face of a prism of angle A (assumed to be small) and emerges normally from the opposite face. If the refractive index of the prism is $\mu$, the angle of incidence i, is nearly equal to

1. $\mu$A

2. $\frac{\mu A}{2}$

3. $A/\mu$

4. $A/2\mu$

A concave mirror of the focal length $f_1$ is placed at a distance of d from a convex lens of focal length $f_2$. A beam of light coming from infinity and falling on this convex lens-concave mirror combination returns to infinity. The distance d must be equal to:

1. $f_1+f_2$

2. $-f_1+f_2$

3. $2f_1+f_2$

4. $-2f_1+f_2$

The magnifying power of a telescope is 9. When it is adjusted for parallel rays the distance between the objective and eyepiece is 20 cm. The focal length of the lenses is :

1. 10 cm, 10 cm

2. 15 cm, 5 cm

3. 18 cm, 2 cm

4. 11 cm, 9 cm

1.  Difference between apparent and real depth of the pond

2.  Mirage on hot summer days

3.  Brilliance of the diamond

4.  Working of optical fibre

A ray of light travelling in a transparent medium of refractive index $\mu$ falls on a surface separating the medium from the air at an angle of incidence of 45 °. For which of the following value of $\mu$, the ray can undergo total internal reflection?

1. $\mu =1.33$

2. $\mu =1.40$

3. $\mu =1.50$

4. $\mu =1.25$

A lens having focal length f and aperture of diameter d forms an image of intensity I . An aperture of diameter $\frac{d}{2}$ in central region of lens is covered by a black paper. The focal length of lens and intensity of the image now will be respectively:

1. f and $\frac{\mathrm{I}}{4}$

2. $\frac{3f}{4} and \frac{I}{2}$

3. f and $\frac{3I}{4}$

4. $\frac{f}{2} and \frac{I}{2}$

Two thin lenses of focal lengths f₁ and f₂ are in contact and coaxial. The power of the combination is :

1.  $\sqrt{\frac{{\mathrm{f}}_1}{{\mathrm{f}}_2}}$

2.  $\sqrt{\frac{{\mathrm{f}}_2}{{\mathrm{f}}_1}}$

3.  $\frac{{\mathrm{f}}_1+{\mathrm{f}}_2}{{\mathrm{f}}_1{\mathrm{f}}_2}$

4.  None of the above

A boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length 10 cm. The diameter of the sun is 1.39 x10⁹ m and its mean distance from the earth is 1.5 x 10¹¹ m. What is the diameter of the sun's image on the paper?

1.  $9.2\times {10}^{-4} \mathrm{m}$

2.  $6.5\times {10}^4 \mathrm{m}$

3.  $6.5\times {10}^{-5} \mathrm{m}$

4.  $12.4\times {10}^{-4} \mathrm{m}$