Question

An object is placed at a distance of 24 cm from a concave mirror. The image obtained on a screen is five times of this object. What is the focal length of the concave mirror?​

Answer 1

Answer:

• 20 cm is the required Focal length.

Explanation:

Given:-

• Object Distance ,u = -24 cm

• Magnification ,m = -5 ( as image is obtained on screen).

To Find:-

• Focal length ,f

Solution:-

As we know that the Magnification is defined as the ratio of height of image to the ratio of height of object.

• m = hi/ho = -v/u

→ m = -v/u

Substitute the value we are

→ -5 = -v/-24

→ -5 = v/24

→ v = -24×5

→ v = -120 cm

• The image is formed 120 cm in front of mirror.

Now, Using Mirror Formula

• • 1/v + 1/u = 1/f

substitute the value we are

→ -1/120 + 1/-24 = 1/f

→ -1/120 -1/24 = 1/f

→ 1/f = -1 -5/120

→ 1/f = -6/120

→ 1/f = -1/20

→ f = -20 cm

• Hence, the focal length of the mirror is 20 cm.

Answer 2

Answer:

Given :-

• Image distance = -24 cm
• Magnification = -5 cm

To Find :-

Focal length

Solution :-

$\huge \bf \: m = \frac{ - v}{u}$

-5 = -v × 24

-5 = -v/24

-5 × 24 = v

-120 = v

Now,

Let's find Focal length

$\huge \tt \: \frac{1}{v } + \frac{1}{u} = \frac{1}{f}$

1/-120 + 1/-24 = 1/f

1/-120 - 1/24 = 1/f

1/f = -1 -5/ 120

1/f = -6/120

1/f = -20

f = 20 × 1

Hence

Focal length is 20 cm.