Question

The focal length of concave Mirror is 30 cm. Find the position of the object in front of

the earth so that the images three times the size of the object.​

Answer 1

Correct Question

The focal length of the concave mirror is 30 cm. Find the position of the object in front of the mirror so that the size of the image is three times the size of the object.

Solution

Given that, the focal length of the concave mirror is 30 cm. (f = -30 cm)

Also given that, the size of the image is three times the size of the object.

Image distance from mirror = 3 × (Object distance from the mirror)

⇒ v = 3u

We have to find the position of the object (u).

Using Mirror formula:

⇒ 1/f = 1/v + 1/u

Substitute the known values,

1/(-30) = 1/3u + 1/u

-1/30 = 1/3u + 1/u

-1/30 = (1 + 3)/3u

-1/30 = 4/3u

-1/10 = 4/u

Cross-multiply them

-1(u) = 4(10)

-u = 40

u = -40 cm

Therefore, the position of the object is 40 cm from the mirror.

Answer 2

$\rule{300}{2}$

GIVEN :-

○ Focal length(f) of a concave mirror = -30 cm.

○ Size of the image is three times the size of the object.(h$\sf{_i}$ = 3h$\sf{_o}$)

TO FIND :-

The position of the object in front of the earth(u).

FORMULAS TO BE USED :-

○ Magnification =

$\displaystyle{\sf{\frac{h_i}{h_o}=\frac{v}{u} }}$

○ Mirror formula :-

$\displaystyle{\sf{\frac{1}{v}+\frac{1}{u}=\frac{1}{f} }}$

SOLUTION :-

We know,

$\displaystyle{\sf{\frac{h_i}{h_o}=\frac{v}{u} }}$

$\displaystyle{\sf{\implies \frac{3h_o}{h_o}=\frac{v}{u} }}$

$\displaystyle{\sf{\implies 3=\frac{v}{u} }}$

$\displaystyle{\sf{\implies 3u=v }}\:\:\:\:\:\:\:\:\cdots(i)$

By using the mirror formula :-

$\displaystyle{\sf{\frac{1}{v}+\frac{1}{u}=\frac{1}{f} }}$

$\displaystyle{\sf{\implies \frac{1}{3u}+\frac{1}{u}=\frac{1}{-30} }}$

$\displaystyle{\sf{\implies \frac{1+3}{3u}=\frac{-1}{30} }}$

$\displaystyle{\sf{\implies \frac{4}{3u}=\frac{-1}{30} }}$

$\displaystyle{\sf{\implies \frac{4}{u}=\frac{-1}{10} }}$

$\displaystyle{\sf{\implies -u=40 }}$

$\large \underline{\boxed{\boxed{\displaystyle{\sf{\implies u=-40\ cm }}}}}$

∴ So, the object is 40 cm in front of the concave mirror. Its magnitude is negative as it is kept in the left side of the mirror.

$\rule{300}{2}$