Question

3 images of coin are seen when the coin is placed in between two mirrors kept at an angle of each other. angle between the mirror are increased 30° more. how many images are now formed​

Answer 1

GiveN :-

• Three images of coin are seen when the coin is placed in between two mirrors kept at an angle of each other.
• Angle between the mirror are increased 30° more.

To FinD :-

• How many images are now formed .

SolutioN :-

According to the question , Three images of coin are seen when the coin is placed in between two mirrors kept at an angle of each other. And the angle is increased by 30 ° . We know the formula to find the number of images formed when the angle between them is given by ,

$\sf:\implies \pink{ n_{(images)}= \dfrac{\theta}{360^o}-1 } \\\\\sf:\implies 3 = \dfrac{\theta}{360^o} -1 \\\\\sf:\implies 3+1 = \dfrac{\theta}{360^o} \\\\\sf:\implies \dfrac{\theta}{360^o} = 4 \\\\\sf:\implies \theta = \dfrac{360^o}{4}\\\\\sf:\implies \underset{\blue{\tt Required \ Intial \ Angle }}{\underbrace{\boxed{\pink{\frak{\theta = 90^o }}}}}$

$\rule{200}2$

★ When the angle is increased by 30° :-

$\sf:\implies n_{(images)}= \dfrac{360 }{90^o + 30^o} \\\\\sf:\implies n_{(images)}=\dfrac{360^o}{120^o}-1 \\\\\sf:\implies n_{(images)}= {3}-1 \\\\\sf:\implies\underset{\blue{\bf Required\ images }}{\underbrace{ \boxed{\pink{\frak{ n_{(images)}= 2 }}}}}$