Question

Some rearview mirrors produce images of cars to your rear that are smaller than they would be if the mirror were flat.Are the mirrors concave or convex? What is a mirrors radius of curvature if cars 20.8 m away appear 0.33x their normal size?

Answer 1

Answer:

Concave mirror,-20.48m

Explanation:

Concave mirrors-This is because the objects are made smaller by the mirror, so they appear farther away.

#we find the image distance from the magnification:

$m=\frac{h_1}{h_o}=\frac{-d_i}{d_o}\\\\+0.33=\frac{-d_i}{20.8}\\\\d_i=-6.864m$

#We find the focal length from:

$({\frac{1}{d_o})}+({\frac{1}{d_i})}=({\frac{1}{f})}\\\\({\frac{1}{20.8})}+({\frac{1}{-6.864})}=\frac{1}{f}\\\\f=-10.24m$

r=2f=-10.24m*2=-20.48m

#The mirror has a negative radius(-20.48m) of curvature since its vertex  lies to the right of the center of curvature