Question

an object 2cm high and right angle to the principal axis of a concave mirror ,is 8cm from the pole . if the radius of the curvature of the mirror is 24cm.find the distance of the image from the pole and it's height.

Answer 1

Answer :

• distance of image from pole is 24 cm ( behind the mirror)
• height of image is 6 cm.

Explanation :

• height of object, h₁ = 2 cm
• position of object, u = -8 cm
• Radius of curvature of Concave mirror, R = -24 cm

[ negative R because radius of curvature of concave mirror is on negative principal axis ]

so,

Since, Radius of curvature is Double of focal length therefore,

→ focal length of concave mirror, f = R / 2

→ f = -24/2 = -12 cm

Now, Let position of image be v

then, using mirror formula

→ 1/f = 1/v + 1/u

→ 1/(-12) = 1/v + 1/(-8)

→ 1/v = 1/(-12) + 1/8

→ 1/v = (-2 + 3)/24

→ v = 24 cm

Now,

Let, height of image be h₂

then,

Using formula for magnification of mirror

→ magnification = -v/u = h₂ / h₁

[ where v is position of image, u is position of object , h₁ is height of image , h₂ is height of object ]

→ -v/u = h₂ / h₁

→ - ( 24 ) / ( - 8 ) = h₂ / 2

→ h₂ = 6 cm

Therefore,

• position of image will be 24 cm behind the mirror. (and distance of image from pole is 24 cm.)
• height of image is 6 cm.