Question

Define centre of curvature of a spherical mirror.
Draw a ray diagram for the image formation by a concave mirror when the size of an object and its image are same.
Write mirror formula.
Calculate speed of light in a medium if refractive index of the medium is $1.5$ and speed of light in vacuum is $3\times {10}^{8}m/s$.

Answer 1

Center of curvature of the Spherical mirror

The point in the center of the sphere from which the mirror was sliced is known as the center of curvature and is denoted by the letter C in the diagram.

This point is equidistant from all points on the reflecting surface of the mirror

The ray diagram for the image formation by a concave mirror when the size of an object and its image are same is given above.

Here, in the diagram if we put the object on the center of curvature then the image will have same size as that of the object.

Mirror Formula is given by :-

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

where,

f = Focal length of the mirror.

v = Distance of image from the mirror.

u = Distance of the object from the mirror.

For Calculating the speed of light in a medium :-

given, n (refractive index)=1.5 and c (speed of light)= $3\times {10}^8\text{m/s}$

therefore using formula;

$RefractiveIndex\left(n\right)=\frac{\text{Speed of light in vacuum(c)}}{\text{Speed of light in the medium(v)}}$

therefore on putting the values,

$1.5=\frac{3\times {10}^8}{v}$

therefore, $v=2\times {10}^8\text{m/sec}$