Question

In the figure shown find the total magnification after two successive reflections first on M1 and then on M2

Answer 1

2 is the total magnification of the two reflections M1 and M2.

Solution:

To find the total magnification, first we need to find the magnification in the two reflections M1 and M2.

First let us calculate the magnification of M1:

Given:

Distance between the object and mirror1, u1  = -30

Focal length, f1=-20

V is the distance of the image from mirror1

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

$\frac{1}{v}-\frac{1}{20}=-\frac{1}{30}$

Therefore we get value of v = -60

Now magnification$\mathrm{M}_{1}=-\frac{v}{u}$

$-\left(\frac{-60}{-30}\right)=-2$

Now calculate the magnification of M2:

Given:

Distance between the object and mirror2, u2 = 20

Focal length, f2= 10

V is the distance of the image from mirror2

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

$\frac{1}{v}+\frac{1}{20}=\frac{1}{10}$

Therefore we get value of v = 20

Now magnification $\mathrm{M}_{2}=-\frac{v}{u}$

$\mathrm{M}_{2}=-\frac{20}{20}=-1$

Total magnification, $\mathrm{M}=\mathrm{M}_{1} \times \mathrm{M}_{2}$

$=(-2) \times(-1)$

=2

Total magnification is 2.

Answer 2

Answer:

2 is the total magnification of the two reflections M1 and M2.

Solution:

To find the total magnification, first we need to find the magnification in the two reflections M1 and M2.

First let us calculate the magnification of M1:

Given:

Distance between the object and mirror1, u1  = -30

Focal length, f1=-20

V is the distance of the image from mirror1

Therefore we get value of v = -60

Now magnification

Now calculate the magnification of M2:

Given:

Distance between the object and mirror2, u2 = 20

Focal length, f2= 10

V is the distance of the image from mirror2

Therefore we get value of v = 20

Now magnification

Total magnification,

=2

Total magnification is 2.