A boy of height 1m stands in front of a convex mirror. His distance from the mirror is equal to its focal length. The height of his image is

Options

A. `0.25 m`
B. `0.33 m`
C. `0.5 m`
D. `0.67 m`

Answer

C

Explanation

Let f be foc al length of the convex mirror. According to new cartesiaan sign convention
Object distance, ` u = - f`, focal length `= + f`
Using mirror formula, `1/u + 1/v = 1/f`
`(1)/(-f)+1/v=1/f` or `1/v=1/f+1/f=2/f` or `v = f/2`
The image is formed at a distance `f/2` behind the mirro. It is virtual image.
Magnification, `m = -(v)/(u) = - ((f//2))/((-f)) = 1/2`
Also, `m = ("Height of image"(h_(I)))/(Height of object(h_(O)))`
`:. h_(I) = mh_(O) = 1/2 (1m) = 0.5 m`