Question

(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 such mirror 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 +24cm.

Answer 1

We have seen in the mirrors of the car written that ‘Object is closer than it seems to appear’ this is because in the car convex mirrors are used. This is because the images formed by the convex mirrors are virtual and erect.

Complete step by step solution:
Step 1: State the type of the mirror and draw a ray diagram also give an explanation as to why one such mirror is put.
The property of a convex mirror is such that the image formed by that is always diminished, erect and virtual. The image formed by a mirror for all positions of the object placed in front of it is always a convex mirror. The image is made between P and F due to a ray of light coming from a distance. See the diagram.
There are many uses for convex mirrors one of the uses of the convex mirror is to reflect the light that is why it is used in front of the car mirrors.

Step 2:
There are two basic types of mirrors one is the curved mirror and another one is the flat mirror. For curved mirrors there are two types one in which the parallel incident rays of light are converged and the second in which the parallel incident rays of light are diverged. Spherical mirror is a misnomer as it is not a complete sphere but a small portion which is cut from an imaginary larger sphere with one cut. When using a spherical mirror there are some reference points taken near and, on the mirror, as to locate the image formed. These are ‘Centre of curvature’, ‘Focal Length ”F” ’, ‘Radius of the curvature ”C” ’, ‘pole “P” ’, etc.

Here the radius of curvature is the distance from the “pole” (P) to the “Center of Curvature” (C).
Find the nature and the focal length of a spherical mirror;
We have been given the radius of the mirror which is +24cm;
The formula for focal length is:
$f = \dfrac{r}{2}$ ;
Where:
r = radius;
f = focal length;
Put in the given value in the above equation:
$f = \dfrac{{24}}{2}$;
The focal length is:
$\Rightarrow f = + 12cm$;
Spherical mirrors are both convex and concave. Here the spherical mirror is convex in nature.

The focal length is +12cm and the nature of the mirror is convex i.e. diverging.

Note: Here explain about the radius of curvature and show the relation between the mirror and the radius of curvature. To determine which of them are convex or concave we have to see their focal length if the focal length is positive then they are convex and if the focal length is negative, they are concave.