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.	\(1.8 \times 10^8 ~\text{m/s}\)	2.	\(2.4 \times 10^8~\text{m/s}\)
3.	\(3.0 \times 10^8~\text{m/s}\)	4.	\(1.2 \times 10^8~\text{m/s}\)

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

1. 1.40

2. 1.50

3. 3.00

4. 1.33

A microscope is focused on a mark on a piece of paper and then a slab of glass of thickness 3 cm and a 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.

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 \(F_1\)${\mathrm{}}_{}$. When the space between the two lenses is filled with glycerin which has the same refractive index as that of glass \((\mu = 1.5),\) then the equivalent focal length is \(F_2\)${\mathrm{}}_{}$. The ratio \(F_1:F_2\) will be:
1. \(3:4\)
2. \(2:1\)
3. \(1:2\)
4. \(2:3\)

A boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of a focal length of \(10\) cm. The diameter of the sun is \(1.39\times10^9\) m and its mean distance from the earth is \(1.5\times10^{11}\) m. What is the diameter of the sun's image on the paper?
 

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 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 \(\frac{I}{4}\)
2.  \(\frac{3f}{4}\) and \(\frac{I}{2}\)
3.  \(f\) and \(\frac{3I}{4}\)
4.  \(\frac{f}{2}\) and \(\frac{I}{2}\)