When an object is placed at \(10\) cm and \(30\) cm from a convex lens, images obtained are of the same magnitude of magnification. The focal length of the lens may be:

1.	\(10\) cm	2.	\(15\) cm
3.	\(20\) cm	4.	\(25\) cm

A concave lens forms the image of an object such that the distance between the object and image is \(10\) cm. If magnification of the image is \(\frac{1}{4},\) the focal length of the lens is:
1. \(-\frac{20}{3}~\text{cm}\)
2. \(\frac{20}{3}~\text{cm}\)
3. \(\frac{40}{9}~\text{cm}\)
4. \(-\frac{40}{9}~\text{cm}\)

A ray of light incident on a prism of angle \(A\) and refractive index \(\mu\) will not emerge out of the prism for any angle of incidence, if:
1. \(\mu>\sin \frac{A}{2}\)
2. \(\mu>\cos{A}\)
3. \(\mu<\frac{1}{\sin A}\)
4. \(\mu>\frac{1}{\sin \frac{A}{2}}\)

In normal adjustment, the angular magnification of an astronomical telescope is \(39\). If length of the tube is \(2\) m, then focal length of the objective and eyepiece are respectively:
1. \(195~\text{cm}, 5~\text{cm}\)
2. \(190~\text{cm}, 10~\text{cm}\)
3. \(20~\text{cm}, 180~\text{cm}\)
4. \(10~\text{cm}, 190~\text{cm}\)

If a light ray is incident normally on face \(AB\) of a prism, then for no emergent ray from second face \(AC\):
\([\mu \rightarrow\) refractive index of glass of prism]

A lens forms an image of a point object placed at distance \(20\) cm from it. The image is formed just in front of the object at a distance \(4\) cm from the object (and towards the lens). The power of the lens is:
1. \(-2.25\) D
2. \(1.75\) D
3. \(-1.25\) D
4. \(1.4\) D