A lens is made of glass having an index of refraction 1.5 . One side of the lens is flat and the other side is convex with a radius $R$. If an object is placed 60 cm , towards the convex side of the lens, the image is formed at

A short straight object of length $l$ lies along the central axis of a spherical concave mirror, at a distance $X$ from the mirror. The focal length of the mirror is $F$. If the length of the image in the mirror is $l^{\prime}$, then ratio $\left(\frac{l^{\prime}}{l}\right)$ is (assume, $l \ll X$ and $l \ll F$ )

Consider a glass prism immersed in a liquid as shown below. The refractive index of glass and liquid is 1.5 and 1.2, respectively. A ray of light enters the prism perpendicular to the face $A B$. The largest value of angle $\theta$ is, if the ray is totally reflected at the face $A C$, then

A thin prism of angle $6^{\circ}$ made of glass of refractive index 1.5 is combined with another prism made of refractive index 1.75 to produce dispersion without deviation. Then, the angle of the second prism is