Physics

Problem

(Long Answer Question) A concave mirror is marketed as a “shaving mirror” because it can produce an erect, magnified image of the user. Let the desired magnification be

+2

(image twice the size of the object and erect). Answer the following. a. (i) Starting from the mirror–magnification relation, derive an expression connecting the object distance

u

and focal length

f

for which the magnification is

+2

. b. (ii) If the mirror has focal length

15\,\text{cm}

, calculate the precise object distance and image distance that satisfy the magnification requirement. c. (iii) The same mirror is now used to project a real image on a screen kept

80\,\text{cm}

in front of the mirror (on the reflecting side). Determine the corresponding object position that will produce this real image on the screen.

Intuitive explanation

A concave mirror's power to magnify and flip images depends entirely on where you place the object relative to the focal point—this is the key to understanding mirror magnification. For an erect, magnified image, you need to position the object between the focal point and the mirror surface, where the mirror acts like a magnifying glass. The magnification formula $m = -v/u$ and the mirror equation $1/f = 1/u + 1/v$ work together: knowing your desired magnification tells you the relationship between object and image distances, which then constrains where the object must sit and what focal length the mirror needs.

Intuitive explanation

Browse the problem library