The mirror in FIGURE P34.65 is covered with a piece of glass. A point source of light is outside the glass. How far from the mirror is the image of this source?

Mirror is concave

Mirror is covered with a piece of Glass

Radius of the mirror R = 4.0 cm

Refractive index of the air, n_air = 1.00

Refractive index of the water, n_water = 1.50

Point source is located at s = 2cm outside the glass

We need to find out the distance between the image and the mirror.

Using the relation between object and image distance with the Refractive index

Object distance s and image distance s' is related as :

$$\begin{gathered} s\text{'}=\frac{n_{glass}}{n_{air}}s \\ Puttingvalues, \\ s\text{'}=\frac{1.50}{1.00}(2.0cm) \\ s\text{'}=3.0cm \end{gathered}$$

The image of the point source formed due to refraction from the glass surface acts as an object to the mirror with object distance $p=\left(3.0+4.0\right)cm=7.0cm$

Using mirror equation,

$$\begin{gathered} \frac{1}{p}+\frac{1}{q}=\frac{1}{f} \\ \left(f=\frac{R}{2}=\frac{4}{2}cm=2cm\right) \\ qistheimagedis\tan ce \\ \frac{1}{q}=\frac{1}{f}-\frac{1}{p} \\ \frac{1}{q}=\frac{p-f}{pf} \\ q=\frac{pf}{p-f} \\ q=\frac{(7.0cm)(2.0cm)}{7.0cm-2.0cm} \\ q=2.8cm \end{gathered}$$