When light of two colours $A$ and $B$ is passed through a plane boundary; $A$ is bent more than $B$. Which colour travels more slowly in the second medium?

Both a spherical mirror and a thin spherical lens have a focal length of $-15 \; cm$. What type of mirror and lens are they?

$(a)$ For the same angle of incidence $45^{\circ}$,the angle of refraction in two transparent media $I$ and $II$ is $20^{\circ}$ and $30^{\circ}$ respectively. Out of $I$ and $II$,which medium is optically denser and why?
$(b)$ Light enters from air to diamond,which has a refractive index of $2.42$. Calculate the speed of light in diamond,if the speed of light in air is $3.00 \times 10^{8} \text{ m s}^{-1}$.

Find the position,nature,and size of the image of an object $3 \, cm$ high placed at a distance of $9 \, cm$ from a concave mirror of focal length $18 \, cm$.

An object is placed $50\, cm$ from a lens that produces a virtual image at a distance of $10\, cm$ in front of the lens. Calculate the focal length of the lens. (in $, cm$)

At what position should an object be placed in front of a concave mirror to obtain a magnification of $(- 2)$?