(a) If the image formed by a mirror for all positions of the object placed in front of it is always diminished, erect and virtual, state the type of the mirror and also draw a ray diagram to justify your answer. Write one use such mirrors are put to and why.(b) Define the radius of curvature of spherical mirrors. Find the nature and focal length of a spherical mirror whose radius of curvature is +24 cm.

(a) If the image formed by a mirror for all positions of the object placed in front of it is always diminished, erect and virtual, then the type of the mirror is Convex.

Such mirrors are used as rear view mirrors in automobiles, as this type of mirror gives erect, and a wider field of view of objects coming behind the automobile.

(b) Radius of curvature of a spherical mirror is the distance between pole $(P)$ and centre of curvature, $(C)$.

Given:

Radius of curvature, $R=+24cm$

To find: Nature and focal length $(f)$ of a spherical mirror.

Solution:

We know that radius of curvature is given as-

$R=2f$

then, 

$f=\frac {R}{2}$

Putting the value of $R$ in the above equation, we get-

$f=\frac {24}{2}$

$f=+12cm$

Thus, the focal length of the spherical mirror is 12cm, and the plus sign implies that the nature of the mirror is concave.

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Updated on: 10-Oct-2022

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