$A$ ray of light enters from a medium with refractive index $n_1$ into a medium with refractive index $n_2$. If the angle of incidence is $\theta_1$ and the angle of refraction is $\theta_2$,then $\sin \theta_1 / \sin \theta_2 = \dots$

$(a)$ Write the relation between $u, v, f$ for lenses and for mirrors,where $u, v, f$ are object distance,image distance,and focal length respectively.
$(b)$ The magnification produced by a concave mirror is $m = +4$. Write the information about the image given by this statement.
$(c)$ Draw a ray diagram for the following and show the formation of the images in the case of a concave mirror when the object is placed:
$(i)$ Between the pole and the focus point.
$(ii)$ At the centre of curvature.

$(a)$ What happens to a ray of light when it travels from one medium to another having equal refractive indices?
$(b)$ State the cause of refraction of light.

What is the focal length of the objective of an astronomical telescope as compared to that of the eyepiece?

For what position of the object does a convex lens form an erect and virtual image?

Rays from the Sun converge at a point $15 \, cm$ in front of a concave mirror. Where should an object be placed so that the size of its image is equal to the size of the object?