Question

A concave mirror is to form an image of the filament of a headlight lamp on a screen 8.50 m from the mirror. The filament is 6.00 mm tall, and the image is to be 37.5 cm tall. Part A: How far in front of the vertex of the mirror should the filament be placed?
Part B: to what radius of curvature should you grind the mirror?

Answer 1

Answer:13.6 cm

Explanation:

Given

v(image distance)=-8.5 m

height of object$(h_1)$=6 mm

height of image $(h_2)$=37.5 cm

and magnification of concave mirror is given by $m=\frac{-v}{u}=\frac{-h_2}{h_1}$

$m=\frac{-37.5\times 10}{6}=-62.5$

$-62.5=\frac{8.5\times 100}{u}$

u=13.6 cm

so object is at a distance of 13.6 cm from mirror.

for focal length

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

$\frac{1}{f}=\frac{-1}{850}+\frac{-1}{13.6}$

$\frac{1}{f}=-0.00117-0.0735$

f=-13.4 cm

thus radius of curvature of mirror is R=2f=26.8 cm