Question

What is the formula for the numbers of image formed in a Plane Mirror.​

Answer 1

Required Answer

The formula for the number of images formed in a plane mirror is $\sf n = \dfrac{{360}^{ \circ}}{\theta} - 1$

1 is subtracted because of the loss of one image due to the overlapping of the two images.

For example :-

If θ = 30°, then the number of images formed in the mirror will be :-

⟼ $\sf n = \dfrac{{360}^{ \circ}}{30} - 1$

⟼ $\sf n = \dfrac{{36 \not0}^{ \circ}}{3 \not0} - 1$

⟼ $\sf n = \dfrac{{36}^{ \circ}}{3} - 1$

⟼ $\sf n = \dfrac{{ \cancel{36}}^{ \circ}}{ \not3} - 1$

⟼ $\sf n = 12 - 1$

⟼ $\sf n = 11$

If θ = 30°, then the number of images formed will be 11.

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Some more formulae :-

• R = 2f
• f = R/2

where,

• f = focal length of the spherical mirror
• R = radius of the curvature

• Linear magnification produced by spherical mirror = $\sf \dfrac{height \: of \: the \: image}{height \: of \: the \: object}$

• Linear magnification when the image is virtual = $\sf{\dfrac{-height~of ~the ~image}{height ~of~ the ~object}}$

• Linear magnification when the image is real = $\sf{\dfrac{height ~of ~the~ image}{height ~of ~the~ object}}$