For a convex mirror, prove that its focal length is equal to half of its radius of curvature?

The ratio of the focal length of spherical mirror to its radius of curvature is-

The focal-length of a spherical mirror of radius of curvature 20cm is

If the focal length of a concave mirror be 15cm then what is its radius of curvature?

A virtual image of half the size of the object is formed by a convex mirror at a distance of 30 cm from the object. What is the radius of curvature of the mirror?

The focal leght of a spherical mirror is 40 cm. What is its radius of curvature ?

If a concave mirror is immersed in water will its focal length change?

What is the radius of curvature of plane mirror?

A concave mirror of focal length 36 cm and a convex mirror of focal length 20 cm are placed face to face on the same axis at a distance of separation 80 cm. An object is placed at a distance 20 cm in front of the convex mirror. Determine the position of the images (i) first by the reflection in convex mirror and then in the concave mirror and (ii) first by the reflection in concave mirror and then in the convex mirror.