Question

An object 4cm high is placed at a distance of 20cm from a

concave mirror of focal length 8cm. By choosing a suitable scale draw a neat ray diagram and calculate the position and size of the image. Also state its characteristics.

Answer 1

Object-size, h = +4.0 cm;
Object-distance, u = – 20.0 cm;
Focal length, f = –8.0 cm;
Image-distance, v = ?
Image-size, h′ = ?
Mirror formula is $\text{(1/v) + (1/u) = 1/f}$

$\frac{1}{v}=\frac{1}{f}-\frac{1}{u}$

$\left(\frac{1}{v}\right)=(-1/8)+\left(1/20\right)$

$v=-\frac{40}{3}=-13.33cm$

The screen should be placed at

$\text{13.33 cm}$

from the mirror. The image is real.

Magnification

$\text{m = h'/h = − v/u = 13.33/(– 20) = – 0.66}$

Height of the image

$\text{h' = mh = (– 0.66)x4 = − 2.66 cm}$

The image in inverted and diminished.