Question

An object 4.0 cm in size, is placed 25.0 cm in front of a concave mirror of focal length 15.0 cm.
(i) At what distance from the mirror should a screen be placed to obtain a sharp image?
(ii) Find the size of the image.
(iii) Draw a ray diagram to show the formation of the image in this case.

Answer 1

Given:
$h_o=+4cm$
$f=-15cm$
$u=-15cm$

(i)
Using mirror formula:
$\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$

$\frac{1}{-25}+\frac{1}{v}=\frac{1}{-15}$
$v=-37.5cm$
Image will be formed at a distance of 37.5 cm from the pole.
(2 marks)
(ii)
Magnification of the mirror is given by:
$m=-\frac{v}{u}=\frac{h_i}{h_o}$
$h_i=-\frac{-v}{u}\times h_o$
$h_i=-\frac{-37.5}{-25}\times 4$
$h_i=-6cm$
Image is 6 cm high. The negative sign indicates that the image is inverted. (1 mark)

(iii)


(2 marks)