Two identical concave mirrors each of focal length f are facing...

Two identical concave mirrors each of focal length

f

are facing each other as shown in the schematic diagram. The focal length

f

is much larger than the size of the mirrors. A glass slab of thickness

t

and refractive index

n_0

is kept equidistant from the mirrors and perpendicular to their common principal axis. A monochromatic point light source

S

is embedded at the center of the slab on the principal axis, as shown in the schematic diagram. For the image to be formed on

S

itself, which of the following distances between the two mirrors is/are correct: Two identical concave mirrors each of focal length f are facing each other as shown in the schematic diagram. The focal

Two identical concave mirrors each of focal length f are facing each other as shown in the schematic diagram. The focal

Options

A $4 f+\left(1-\frac{1}{n_0}\right) t$
B $2 f+\left(1-\frac{1}{n_0}\right) t$
C $4 f+\left(n_0-1\right) t$
D $2 f+\left(n_0-1\right) t$

Correct answer

A. $4 f+\left(1-\frac{1}{n_0}\right) t$

Step-by-step solution

\begin{aligned} & \frac{S-t}{2}+\frac{t}{2 n_0}=2 f \\ & S+t\left(\frac{1}{n_0}-1\right)=4 f \\ & S=4 f+\left(1-\frac{1}{n_0}\right) t\end{aligned}

Also

\begin{aligned} & \frac{\mathrm{S}-\mathrm{t}}{2}+\frac{\mathrm{t}}{2 \mathrm{n}_0}=\mathrm{f} \\ & \mathrm{S}=2 \mathrm{f}+\left(1-\frac{1}{\mathrm{n}_0}\right) \mathrm{t}\end{aligned}

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