The magnification of a compound microscope for the final image at the least distance of distinct vision is \(90\). The magnification of the objective lens is \(15\). The value of the focal length of the eyepiece will be: 
1. \(5\) cm
2. \(6\) cm
3. \(\dfrac{1}{6}\) cm
4. \(12\) 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:

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]