Two lenses have powers of $(a) +2 \text{ D}$ and $(b) -4 \text{ D}$. Find the nature and focal length of each lens.

$A$ ray of light is incident obliquely on a glass slab. Draw a ray diagram showing the path of the light ray. Clearly,mark the angle of incidence,angle of refraction,angle of emergence,and lateral displacement of the ray. Give a formula to find the refractive index of the glass slab in terms of the angle of incidence and the angle of refraction.

$A$ convex lens forms a real and inverted image of a needle at a distance of $50\, cm$ from the lens. Where should the needle be placed in front of the convex lens so that this image is of the same size as the object? Also, find the power of the lens.

Why does a light ray incident on a rectangular glass slab immersed in any medium emerge parallel to itself? Explain.

State the sign convention used to measure the length of the image and the object.

Magnification produced by a rear-view mirror fitted in vehicles $....$