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?
 

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