Question

2. A 10-cm high object is placed in front of a convex mirror with focal length 20 cm. Determine the image height if the object distance is (a) 10 cm (b) 30 cm (c) 40 cm (d) 50 cm ​

Answer 1

Answer:

Given that -

height of object - 10 cm

focal length - -20 cm

height of image - ?

By Mirror formula,

1 / F = 1 / V + 1 / U

I case -

U = -10 cm

1 / -20 = 1 / V - 1 / 10

1 / V = 1 / 10 - 1 / 20

1 / V = ( 2 - 1 ) / 20 = 1 / 20

V = 20 cm

M = - V / U = Hi / Ho

- 20 / - 10 = Hi / 10

Hi = 2 x 10 = 20 cm

hence height of image is 20 cm

II case - U = - 30 cm

1 / -20 = 1 / V - 1 / 30

1 / V = 1 / 30 - 1 / 20

1 / V = ( 2 - 3 ) / 60 = -1 / 60

V = - 60 cm

M = - V / U = Hi / Ho

- ( - 60) / -20 = Hi / 10

Hi = -3 x 10 = -30 Cm

hence height of image is 30 cm

III case - U = - 40 cm

1 / -20 = 1 / V - 1 / 40

1 / V = 1 / 40 - 1 / 20

1 / V = ( 1 - 2 ) / 40 = - 1 / 40

V = - 40 cm

M = - V / U = Hi / Ho

- ( -40 ) / - 40 = Hi / 10

Hi = -1 x 10 = -10 cm

hence the height of image is 10 cm

IV case - U = - 50 cm

1 / - 20 = 1 / V - 1 / 50

1 / V = 1 / 50 - 1 / 20

1 / V = ( 2 - 5 ) / 100 = -3 / 100

V = -100 / 3 = - 33.3cm

M = - V / U = Hi / Ho

- ( -100) / -50 = Hi / 10

Hi = - 2 x 10 = - 20 cm

hence the height of image is 20 cm

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Answer 2

Answer:

Explanation:

Given :-

Object height, h(o) = 10 cm

Focal length, f = 20 cm

To Find :-

Image height, h(i) = ??

Formula to be used :-

Mirror formula, 1/v + 1/u = 1/f

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

Solution :-

(a) u = - 10 cm

From mirror formula, we have

1/v + 1/u = 1/f

⇒ 1/v = 1/f - 1/u

⇒ 1/v = 1/20 - 1/- 10

⇒ 1/v = 1 + 2/20

⇒ 1/v = 3/20

⇒ v = 20/3 cm

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

⇒ h(i) = 2 × 10/3

⇒ h(i) = 20/3 cm

Hence, the image height is 20/3 cm.

(b) u = - 30 cm

From mirror formula, we have

1/v + 1/u = 1/f

⇒ 1/v = 1/f - 1/u

⇒ 1/v = 1/20 - 1/- 30

⇒ 1/v = 3 + 2/60

⇒ 1/v = 5/60

⇒ v = 12 cm

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

⇒ h(i) = 12 × 10/30

⇒ h(i) = 4 cm

Hence, the image height is 4 cm.

(c) u = - 40 cm

From mirror formula, we have

1/v + 1/u = 1/f

⇒ 1/v = 1/f - 1/u

⇒ 1/v = 1/20 - 1/- 40

⇒ 1/v = 2 + 1/40

⇒ 1/v = 3/40

⇒ v = 40/3 cm

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

⇒ h(i) = 4 × 10/12

⇒ h(i) = 10/3 cm

Hence, the image height is 10/3 cm.

(d) u = - 50 cm

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

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.