Question

A
10-cm high object is placed in
front of
a convex mirror with focal
length 20cm. Determine the image
height if the object
distance is
50cm​

Answer 1

Answer:

Explanation:

Given:-

Object height, h(o) = 10 cm

Focal length, f = 20 cm

Object distance, u = - 50 cm

To Find:-

Image height, h(i) = ??

Formula to be used:-

Mirror formula, i.e, 1/v + 1/u = 1/f

Magnification, m = - v/u = h(i)/h(o)

Solution :-

From mirror formula, we have

1/v + 1/u = 1/f

⇒ 1/v = 1/f - 1/u

⇒ 1/v = 1/20 - 1/- 50

⇒ 1/v = 5 + 2/100

⇒ 1/v = 7/100

⇒ v = 100/7 cm

Now, Magnification, m = - v/u = h(i)/h(o)

⇒ h(i) = 2 × 10/7

⇒ h(i) = 20/7 cm.

Hence, the image height is 20/7 cm.

Answer 2

▓▓GIVEN▓▓

◙ Size of the object ( $\sf{h_o}$ ) = 10 cm

◙ Focal length (f) = 20 cm

(Positive as it is a convex mirror)

◙ Object distance (u) = -50 cm

(Negative as object is placed in front of the mirror, i.e. left side)

▓▓TO FIND▓▓

The height of the image ( $\sf{h_i}$ ).

▓▓SOLUTION▓▓

As we know the mirror formula :-

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

Substituting the values :-

$\displaystyle{\sf{\implies \frac{1}{v}+\frac{1}{-50}=\frac{1}{20} }}$

$\displaystyle{\sf{\implies \frac{1}{v}=\frac{1}{20}+\frac{1}{50} }}\\\\\\\displaystyle{\sf{\implies \frac{1}{v}=\frac{5+2}{100} }}\\\\\\\displaystyle{\sf{\implies \frac{1}{v}=\frac{7}{100} }}\\\\\\\displaystyle{\sf{\implies v=\frac{100}{7}\ cm }}$

We also know that,

$\displaystyle{\sf{Magnification=\frac{-v}{u}=\frac{h_i}{h_o} }}\\\\\displaystyle{\sf{\implies \frac{\frac{-100}{7} }{-50}=\frac{h_i}{10} }}\\\\\displaystyle{\sf{\implies \frac{2}{7}=\frac{h_i}{10} }}\\\\\boxed{\boxed{\displaystyle{\sf{\implies h_i=\frac{20}{7}\ cm }}}}\:\:\:\:\:\:\:\: \cdots \mathbf{ANSWER}$

Therefore, the height of the image is 20/7 cm.