When a biconvex lens of glass having refractive index 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 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. \(2f_1 +f_2\)
3. \(-2f_1 +f_2\)

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 lengths of lenses are:

1.  Difference between apparent and real depth of the pond

2.  Mirage on hot summer days

3.  Brilliance of diamond

4.  Working of optical fiber

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.  $12.4\times {10}^{-4} \mathrm{m}$