Question

an object of 2 cm height is placed ata diatance of 20 cm from the mirror of 10 cm focal length. Find the position and size of the mirror.

Answer 1

Answer:

Given -

• size of object, $\sf{h}_{o}$ = 2 cm
• Focal length, f = - 10 cm
• Object distance, u = -20 cm

To find -

• Size of the mirror, $\sf{h}_{i}$
• Image formula, v

Solution -

$\\ \sf \: \dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u} \\ \\ \\ \implies \sf \: \dfrac{1}{ - 10} = \dfrac{1}{v} + \dfrac{1}{ - 20} \\ \\ \\ \implies \sf \: \dfrac{1}{v} = \frac{ - 2 + 1 }{20 } \\ \\ \\ \implies \sf \: \dfrac{1}{v} = \dfrac{ - 1}{20} \\ \\ \\ \implies \sf \blue{v = - 20 \: cm}$

• Image distance, v = -20 cm

$\\ \bold{ \underline{Magnification \: \: (m) : - }} \\ \\ \sf \: \frac{h_i}{h_o} = \frac{20}{ - 20} \\ \\ \\ \implies \sf \: - 1 \times 2 = - 2 \: \: cm \:$

Image will be real & inverted.