Question

If $x,y,z,t$denote object distance, image distance, focal length and radius of curvature in the case of a mirror respectively, $\frac{1}{x}+\frac{1}{y}=\frac{1}{z}=\frac{2}{t}$ is true for

• A. convex mirror only
• B. concave mirror only
• C. plane mirror only
• D. all types of mirror

Answer 1

The correct option is D

all types of mirror

1. The object distance, image distance, and focal length are connected in ray optics as
   $\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
   Where, $u$ is the object distance, $v$ is the image distance, $f$ is the focal length, and $R$ is the spherical mirror's radius of curvature.
2. The radius of curvature is the distance between the vertex and the center of curvature ($R$). The mirror's radius of curvature is equal to the radius of the sphere from which it was cut.
3. The focal length is the distance between the mirror and the focal point ($f$).
4. The focal length would be one-half the radius of curvature since the focal point is the midway of the line segment connecting the vertex and the center of curvature.
5. We know that the mirror formula is applicable for convex, concave, and plan mirrors. Hence, it is applicable to all types of mirrors.

So, the correct option is D