Question

Find the difference in positions of images by two mirrors approximately

Ans is 35cm pls show working

Answer 1

Given that,

Focal length = 20 cm

Object distance = 15 cm

For convex lens ,

The focal length is positive.

We need to calculate the image distance

Using formula of mirror

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

Where, f = focal length

v = image distance

u = object distance

Put the value into the formula

$\dfrac{1}{20}=\dfrac{1}{v}+\dfrac{1}{-15}$

$\dfrac{1}{v}=\dfrac{1}{20}+\dfrac{1}{15}$

$\dfrac{1}{v}=\dfrac{7}{60}$

$v=\dfrac{60}{7}\ cm$

For concave lens ,

The focal length is negative.

We need to calculate the image distance

Using formula of mirror

$\dfrac{1}{f}=\dfrac{1}{v'}+\dfrac{1}{u}$

Put the value into the formula

$\dfrac{1}{-20}=\dfrac{1}{v'}+\dfrac{1}{-15}$

$\dfrac{1}{v'}=\dfrac{1}{-20}+\dfrac{1}{15}$

$\dfrac{1}{v'}=\dfrac{1}{60}$

$v'=60\ cm$

We need to calculate the difference in positions of images by two mirrors

Using formula for difference of positions

$v''=v'-v$

Put the value into the formula

$v''=60-\dfrac{60}{7}$

$v''=51.4\ cm$

According to given options,

The nearest value of the difference in positions of images is 70 cm.

Hence, The difference in positions of images by two mirrors approximately 70 cm.

(4) is correct option.

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Topic : optics

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