Question

A bottle 6.0 cm tall is located 69 cm from the concave surface of a mirror with a radius of curvature of 43 cm .

1. Where is the image located? Express your answer using two significant figures. 2. What is its height? 3. What are its characteristics? Real, virtual, upright or inverted?

Answer 1

Answer:

Given, height of the object ho = 6.0 cm, object distance u = 69 cm and radius of curvature R = 43 cm

Focal length of the concave mirror is f = R/2 = 43 cm/2 = 21.5 cm

(1) Using the expression 1/f = 1/u + 1/v

Therefore, the image distance v = u.f / u - f = (69 cm) (21.5 cm) / [69 cm - 21.5 cm] = 31.23 cm. This is positive value value. If the image distance is positive then the image will be real image.

(2) Now, hi/ho = - v/u

Therefore, hi = (-v/u) ho = (-31.23 cm/69 cm) (6.0 cm) = -2.71 cm.

(3) If the image height is negative, then the image will be inverted image.