Question

Find the number of images formed if the angle between them is:-
i-50°
ii-60°
iii-45°
iv-30°
v-90°​

Answer 1

Answer:

We can find the number of images formed if we know the angle between the plane mirrors. This is given by formula: n= (360/ ϴ) - 1 if 360 /ϴ is even. n= 360/ ϴ if it comes odds.

Answer 2

$\large\underline{\sf{Solution-}}$

We know,

Number of images formed by two plane surfaces inclined at an angle θ depends upon the value of n, where n is evaluated as n = $\dfrac{360 \degree}{\theta}$.

Now

• Case :- 1 If n is even then number of images formed = n - 1

• Case :- 2 If n is odd then number of images formed is n

• Case :- 3 If n is in fractions, then number of images formed is the integral part of the fraction.

Let's solve the problem now!!

$\large\underline{\sf{Solution-i}}$

$\rm \: \theta \: = \: 50 \degree$

So,

$\rm \: n = \: \dfrac{360\degree }{50\degree }$

$\rm \: n = \: \dfrac{36 }{5}$

$\rm \: n = \: 7\dfrac{1}{5}$

$\rm\implies \:\boxed{ \rm{ \:Number \: of \: images \: = \: 7 \: }}$

$\large\underline{\sf{Solution-ii}}$

$\rm \: \theta \: = 60\degree$

So,

$\rm \: n = \: \dfrac{360\degree }{60\degree }$

$\rm \: n = 6$

So,

$\rm\implies \:\boxed{ \rm{ \:Number \: of \: images \: = \: 6 - 1 = 5\: }}$

$\large\underline{\sf{Solution-iii}}$

$\rm \: \theta \: = 45\degree$

So,

$n = \: \dfrac{360\degree }{45\degree }$

$\rm \: n \: = \: 8$

Thus,

$\rm\implies \:\boxed{ \rm{ \:Number \: of \: images \: = \: 8 - 1\: = 7 }}$

$\large\underline{\sf{Solution-iv}}$

$\rm \: \theta \: = 30\degree$

So,

$\rm \: n = \: \dfrac{360\degree }{30\degree }$

$\rm \: n = 12$

Thus,

$\rm\implies \:\boxed{ \rm{ \:Number \: of \: images \: = \: 12 - 1 = 11 \: }}$

$\large\underline{\sf{Solution-v}}$

$\rm \: \theta \: = 90\degree$

So,

$\rm \: n = \: \dfrac{360\degree }{90\degree }$

$\rm \: n \: = \: 4$

Thus,

$\rm\implies \:\boxed{ \rm{ \:Number \: of \: images \: = \: 4 - 1 = 3\: }}$