Question

`At what distance from one's face should a pocket convex mirror 5 cm in cross-section be held to see all the face if the focal length of the mirror is 7.5 cm and the length of the face is 20 cm. (Assume eye of face is at centre of face)

• A. 15 cm
• B. 30 cm
• C. 45 cm
• D. 20 cm

Answer 1

Answer: (A)

15 cm

Answer 2

=

$\frac { 1 } { \mathrm { f } }$ =

= $\frac { 1 } { - x } + \frac { 1 } { v }$

v = $\frac { \mathrm { fx } } { \mathrm { f } + \mathrm { x } }$

a₂ = = f

Length of face image is l₂ = m × O

=

l₂ = × l₁

=

= $\frac { 2 \mathrm { f } + \mathrm { x } } { \mathrm { f } \times \ell _ { 1 } }$

– 2 f = x

x = $\frac { 7.5 \times 20 } { 5 } - 7.5 \times 2$

x = 30 – 15 = 15