An object is placed at an unknown distance from a convex objective lens of focal length 5 cm . The objective lens forms a real image which acts as an object for a convex eyepiece of focal length 6.25 cm . The distance between the objective and eyepiece is 20 cm . The microscope is adjusted so that the final image is formed at the least distance of distinct vision $(25 \mathrm{~cm})$. Which of the following is correct?

A. Object distance $=7.5 \mathrm{~cm}$; Total magnification $=10$

B. Object distance = 10 cm ; Total magnification = 20

C. Object distance $=5 \mathrm{~cm}$; Total magnification $=20$

D. Object distance = 2.5 cm ; Total magnification = 10

If a clear liquid has a refractive index of 1.45 and a transparent solid has a refractive index of 2.9 , then for total internal reflection to occur at the interface between the two media; which of the following is correct?

A. The ray must travel from transparent solid to liquid at an angle of $15^{\circ}$

B. The ray must travel from liquid to transparent solid at an angle of $45^{\circ}$

C. The ray must travel from transparent solid to liquid at an angle of $30^{\circ}$

D. The ray must travel from liquid to transparent solid at an angle of $60^{\circ}$

In the normal adjustment of an astronomical telescope, the objective and eyepiece are 36 cm apart. If the magnifying power of the telescope is 8 , find the focal lengths of the objective and eyepiece.

A beam of incident parallel light falls on a diverging lens of focal length 20 cm in magnitude. If a converging lens of focal length 15 cm in magnitude is placed at a distance of 10 cm to the right of the diverging lens on the other side, then, the final image formed is: