Two identical thin plano-convex glass lenses (refractive index = \(1.5\)) each having radius of curvature of \(20\) cm are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of a refractive index of \(1.7\). The focal length of the combination is:
1. \(-20\) cm
2. \(-25\) cm
3. \(-50\) cm
4. \(50\) cm

If the focal length of the objective lens is increased then the magnifying power of:

The angle of a prism is \(A\). One of its refracting surfaces is silvered. Light rays falling at an angle of incidence \(2{A}\) on the first surface return back through the same path after suffering reflection at the silvered surface. The refractive index \(\mu,\) of the prism, is:
1. \(2\text{sin}A\)
2. \(2\text{cos}A\)
3. \(\dfrac{1}{2}\text{cos}A\)
4. \(\text{tan}A\)

For a normal eye, the cornea of the eye provides a converging power of \(40~\text{D}\) and the least converging power of the eye lens behind the cornea is \(20~\text{D}\). Using this information, the distance between the retina and the cornea-eye lens can be estimated to be:
1. \(2.5~\text{cm}\)
2. \(1.67~\text{cm}\)
3. \(1.5~\text{cm}\)
4. \(5~\text{cm}\)

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:

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. \(11~\text{cm}, ~9~\text{cm}\)