Answer to Question #263630 in Optics for Rethabile

Question

Question 13 (4 points)

A concave mirror has a radius of curvature of 40.5 cm and is positioned at a distance such that the upright image of a person's face is 1.5 times the size of his face. How far is the mirror from the person's face?

Question 13 options:

A) 

No option is correct

B) 

+4.75 cm

C) 

+ 5.75 cm

D) 

+3.75 cm

E) 

+ 6.75 cm

Answer 1

$r=40.5 \; cm \\ f = \frac{r}{2} = 20.25 \;cm \\ v=-mu \\ v = -1.5u \\ \frac{1}{u} + \frac{1}{v} = \frac{1}{f} \\ \frac{1}{u} - \frac{1}{1.5u} = \frac{1}{20.25} \\ 1.5 -1 = \frac{1.5u}{20.25} \\ 0.5 = \frac{1.5u}{20.25} \\ 1.5u = 10.125 \\ u = 6.75 \;cm$

Answer: E) +6.75 cm