Question

a) What is the relation between focal length & radius of curvature? Calculate the focal length of convex lens having radius of curvature as 2 m. [2 Marks]

b) A candle, 4 cm in size is placed at 25 cm in front of a concave mirror of focal length 15 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Find the nature and size of the image.
[3 Marks]

Answer 1

a) For a spherical mirror the principal focus (F) lies exactly mid-way between the pole (P) and centre of curvature (C). So, the focal length (f) of a spherical mirror is equal to half of its radius of curvature (R).
f=R/2 [1 Mark]
R= 2 m= 200 cm (Given)
f=?
We know that
f=R/2
=200/2
f =100 cm
So, focal Length is 100 cm= 1m.
[1 Mark]
b) Given:
$h_o=+4cm$
$f=-15cm$
$u=-15cm$ [1 Mark]

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.
[1 Mark]
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]