Question

the focal length of a convex mirror is 10 cm. if an object of height 2 cm is placed at a distance of 20 cm from the mirror then the height of the image is​

Answer 1

Answer:

• Height of Image is 6 cm.

Explanation:

Given:-

• Focal Length ,f = 10 cm
• Object height ,ho = 2 cm
• Object distance ,u = -20 cm

To Find:-

• Image Height ,hi

Solution:-

Firstly we calculate the image position . Using Mirror Formula

• 1/v + 1/u = 1/f

where,

• v is the Image Position
• u is the object distance
• f is the focal length

Substitute the value we get

→ 1/v = 1/f - 1/u

→ 1/v = 1/10 - 1/(-20)

→ 1/v = 1/10 + 1/20

→ 1/v = 2+1/20

→ 1/v = 3/20

→ v = 20/3 cm

• Hence, the image position is 20/3 cm behind the mirror.

Now, using Magnification Formula

• m = hi/ho = -v/u

substitute the value we get

→ hi/2 = -20/3/(-20)

→ hi/2 = 20/3/20

→ hi/2 = 3

→ hi = 6 cm

• Hence, the height of image is 6 cm.

Answer 2

Answer:

Given :-

• Focal length = 10 cm
• Height of object = 2 cm
• Object Distance = -20 cm

To Find :-

Height of mirror

Solution :-

As we know that

1/v + 1/u = 1/f

1/v = 1/10 - 1/-20

1/v = 1/10 + 1/20

1/v = 2+1/20

1/v = 3/20

v = 20/3

Now,

hi/ho = -v/u

hi/2 = -20/3/-20

hi/2 = 3

hi = 3 × 2

hi = 6 cm

HENCE :-

Height of image is 6 cm.