Question

19. A concave mirror has a focal length of \( 4 cm \) and an object \( 2 cm \) tall is placed \( 9 cm \) away from it. Find the nature, position and size of the image formed. 20. When an object is placed \( 20 cm \) from a concave mirror, a real image magnified three times is formed. Find: (a) the focal length of the mirror.

Answer 1

f = -4 cm, h_o = 2 cm, u = -9 cm

Using mirror formula

\({1\over f} = {1\over v}+{1\over u} \)

\({1\over -4} = {1\over v}+{1\over -9}\)

\({1\over v} = {1\over 9}-{1\over 4}\)

\({1\over v} = {4-9\over 36}\)

\(v=-7.2 cm\)

Now, using the magnification formula, we get 

\(m = {h_{i}\over h_{o}}= -{v\over u}\)

\({h_{i}\over h_{o}} = -{(-7.2)\over -9}\)

\({h_{i}\over 2} = -{(-7.2)\over -9}\)

\(h_{i}={{2\times(-7.2)}\over -9}\)

\(h_{i}= -1.6cm\)

Thus, the height of the image '\(h_{i}\)' is 1.6 cm.

Thus, the image is real, inverted and small in size.