$A$ 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 $\sin \theta_1 / \sin \theta_2 = \dots$

The image of a candle flame formed by a lens is obtained on a screen placed on the other side of the lens. If the image is three times the size of the flame and the distance between the lens and the image is $80 \, cm$,at what distance should the candle be placed from the lens? What is the nature of the image at a distance of $80 \, cm$ from the lens (in $, cm$)?

State the relation between object distance,image distance,and focal length of a concave or convex mirror. $A$ concave mirror produces a two times magnified real image of an object placed at $10 \ cm$ from it. Find the position of the image.

If the focal length of a spherical mirror is $20 \ cm$,what is its radius of curvature (in $cm$)?

Which of the following can produce a magnification of $+5$ as well as $-5$?

An object of height $5 \, cm$ is placed perpendicular to the principal axis of a concave lens of focal length $10 \, cm$. If the distance of the object from the optical centre of the lens is $20 \, cm$,determine the position,nature,and size of the image formed using the lens formula.