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. \(\frac{A}{\mu}\)
4. \(\frac{A}{2\mu}\)

A concave mirror of the focal length \(f_1\) is placed at a distance of \(d\) from a convex lens of focal length \(f_2\)${\mathrm{}}_{}$. 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 \(20~\text{cm}\). The focal length of the lenses is:
1. \(10~\text{cm}, ~10~\text{cm}\)
2. \(15~\text{cm}, ~5~\text{cm}\)
3. \(18~\text{cm}, ~2~\text{cm}\)
4. \(11~\text{cm}, ~9~\text{cm}\)

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 \(45^{\circ}\). 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 \(\frac{I}{4}\)
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 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?