Question

An object is placed at a distance of 12 cm in front of a concave mirror of focal length 15 cm. Find the position of image.
 A)V = 20/3 cm 
B)V =1/60 cm 
C)V = 3/20 cm 
D)V = 60 cm​

Answer 1

Answer :

Distance of object = 12

Focal length = 15cm

Type of mirror : concave

We have to find position of image$.$

★ Focal length of concave mirror is taken negative and that of convex mirror is taken positive.

Position of image can be calculated by using mirror formula.

• 1/u + 1/v = 1/f

→ u denotes distance of object

→ v denotes distance of image

→ f denotes focal length

By substituting the values,

➠ 1/(-12) + 1/v = 1/(-15)

➠ 1/v = -1/15 + 1/12

➠ 1/v = (-12 + 15)/180

➠ v = 180/3

➠ v = 60cm

★ Nature and size of image :

• Virtual
• Erect
• Enlarged

Cheers!

Answer 2

60 cm is the required answer.

GIVEN:

Object distance, u = -12 cm

Focal length of concave mirror, f = -15 cm

TO FIND:

Position of the image, image distance, v

FORMULA:

According to mirror formula

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

SOLUTION:

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

$\frac{1}{-15} =\frac{1}{v} +\frac{1}{-12} \\\\-\frac{1}{15} =\frac{1}{v} -\frac{1}{12} \\\\-\frac{1}{15} +\frac{1}{12} =\frac{1}{v} \\\\\frac{1}{v} =\frac{-12+15}{(15\times12)} \\\\\frac{1}{v} =\frac{3}{15\times12} \\\\v = \frac{15\times12}{3} \\\\v = \frac{15}{3} \times12\\\\v = 5\times12\\\\v = 60\: cm$

ANSWER:

The image is placed at a distance of 60 cm to the right of concave mirror.

IMPORTANT POINTS:

• The focal length of concave mirror is negative because the focus of concave mirror is at left of the principal centre.

• The object is placed infront the mirror, (which refers to the left side), its distance is taken negative.

• Since the image distance is positive, image is formed at the right of the mirror.

• The image is a virtual image , because the incident rays do not actually meet. They are appeared to meet at the other side of the mirror.