A ray of light traveling 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 . 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 image now will be respectively :

1. f and $\frac{1}{4}$

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.  $12.4\times {10}^{-4} \mathrm{m}$

A small coin is resting on the bottom of a beaker filled with a liquid. A ray of light from the coin travels up-to-the surface of the liquid and moves along its surface(see figure). 
 
How fast is the light traveling in the liquid?

1. $1.8\times {10}^8 m/s$

2. $2.4\times {10}^8 m/s$

3. $3.0\times {10}^8 m/s$

4. $1.2\times {10}^8 m/s$

The frequency of a light wave in a material is 2×10¹⁴ Hz and wavelength is 5000 Å. The refractive index of material will be:

1. 1.40

2. 1.50

3. 3.00

4. 1.33

A microscope is focussed on a mark on a piece of paper and then a slab of glass of thickness 3 cm and refractive index 1.5 is placed over the mark. How should the microscope be moved to get the mark in focus again?

1. 1 cm upward

2. 4.5 cm downward

3. 1 cm downward

4. 2 cm upward

A convex lens and a concave lens, each having the same focal length of 25 cm, are put in contact to form a combination of lenses. The power in dioptres of the combination is :

1. 25

2. 50

3. infinite

4. zero

Pick the wrong statement in the context with a rainbow.

1. Rainbow is a combined effect of dispersion, refraction, and reflection of sunlight.

2. When the light rays undergo two internal reflections in a water drop, a secondary rainbow is formed.

3.  The order of colors is reversed in the secondary rainbow.

4. An observer can see a rainbow when his front is towards the sun.

Two similar thin equi-convex lenses, of focal length f each, are kept coaxially in contact with each other such that the focal length of the combination is $F_1$. When the space between the two lenses is filled with glycerin which has the same refractive index ($\mu =1.5$) as that of glass, then the equivalent focal length is $F_2$. The ratio $F_1:F_2$ will be:

1. 3 : 4

2. 2 : 1

3. 1 : 2

4. 2 : 3