Question

Select the correct statement about the magnitude of the magnification of a concave mirror if the object is beyond the center of curvature C (do > r).

A) The magnitude of the magnification of a concave mirror is equal to 1.
B) The magnitude of the magnification of a concave mirror is greater than 1.
C) The magnitude of the magnification of a concave mirror is less than 1.

Answer 1

Answer:

c) The magnitude of the magnification of a concave mirror is less than 1

Explanation:

we know

the mirror formula is given as:

$\frac{1}{v}+\frac{1}{u}=\frac{2}{r}$   ..............(1)

also

magnification (m) of mirror is given as:

$m=\frac{-v}{u}$ . ..... (2)

where,

v = image distance

u = object distance

r = Radius of curvature of the mirror

Now

from (2)

$v=-mu$

substituting in (1), we get

$\frac{1}{u}(\frac{1}{-m}+1)=\frac{2}{r}$

or

$\frac{1}{2}(1-\frac{1}{m})=\frac{u}{r}$     ..............(3)

now it is given that object is beyond the center of the the curvature

thus,

⇒$\frac{u}{r}>1$     ................(4)

comparing the (3) and (4), we have

$\frac{1}{2}(1-\frac{1}{m})>1$

or

$(1-\frac{1}{m})>2$

or

$-\frac{1}{m}>2-1$

or

$-\frac{1}{m}>1$

⇒$m<-1$

Hence, the magnification is less than 1