Question

Define the principal focus of a concave mirror. A convex mirror used for rearview on an automobile has a radius of curvature of 3.00 m. If a bus is located at 5.00 m from the mirror. Find the position, nature and size of the image. Draw ray diagram.

Answer 1

The rays of light parallel and close to the principal axis of the mirror after reflection pass through a point on the principal axis, this point is called principal focus of the concave mirror.

Given,

Radius of curvature R = + 300 m

Distance of object u =- 500 m

Distance of image υ = ?

Height of image h’ =?

∵ f = \(\frac{R}{2}\) = \(\frac{3.00\ m}{2}\) = +1.50 m

Since \(\frac{1}{u}\) + \(\frac{1}{v}\) = \(\frac{1}{f}\)

or \(\frac{1}{v}\) = \(\frac{1}{f}\) − \(\frac{1}{u}\)

= \(\frac{1}{1.50}-\frac{1}{(-5.00)}\)

= \(\frac{1}{1.50}+\frac{1}{5.00}\)

⇒ ν = \(+\frac{15}{13}\) = +1.15 m

Magnification,

m = \(\frac{h'}{h}\) = \(\frac{−v}{u}\) = \(-\frac{1.15 m}{−5.00 m}\)

= +0.23

The image is virtual, erect and smaller in size by a factor of 023.