$A$ $4.5\, cm$ needle is placed $12\, cm$ away from a convex mirror of focal length $15\, cm$. Give the location of the image and its magnification.

$A$ dice is placed with one of its edges parallel to the principal axis between the principal focus $(F)$ and the centre of curvature $(C)$ of a concave mirror. Then the final image has the shape of

Draw ray diagrams showing the image formation by a convex lens when an object is placed:
$(a)$ Between optical centre and focus of the lens.
$(b)$ Between focus and twice the focal length of the lens.
$(c)$ At twice the focal length of the lens.
$(d)$ At infinity.
$(e)$ At the focus of the lens.

$A$ student focused the image of a candle flame on a white screen using a convex lens. He noted down the positions of the candle,screen,and lens as follows:
Position of candle $= 12.0 \, cm$
Position of convex lens $= 50.0 \, cm$
Position of the screen $= 88.0 \, cm$
$(i)$ What is the focal length of the convex lens?
$(ii)$ Where will the image be formed if he shifts the candle towards the lens to a position of $31.0 \, cm$?

Which of the following is the correct general form of Snell's law?

$(a)$ 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.