Question

Determine the image distance and image height for a 5.00-cm tall object placed 20.0 cm from a concave mirror having a focal length of 15.0 cm.(v= 60.0 cm and hi = -15.0 cm)

Answer 1

Answer :-

→ Distance of the image is 60 cm .

→ Height of the image is 15 cm .

Explanation :-

We have :-

→ Height of the object = 5 cm

→ Distance of the object = 20 cm

→ Focal length of the mirror = 15 cm

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As per to sign convention [concave mirror] :-

• u = -20 cm

• f = -15 cm

According to mirror formula, we have :-

1/v + 1/u = 1/f

⇒ 1/v = 1/f - 1/u

⇒ 1/v = (-1)/15 - (-1)/20

⇒ 1/v = (-4 + 3)/60

⇒ 1/v = -1/60

⇒ -v = 60

⇒ v = -60 cm

[Negative sign of 'v' shows that the image is formed in front of the mirror.]

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Now, from the formula of magnification of a spherical mirror :-

m = -(v/u) = hᵢ/hₒ

⇒ -(v/u) = hᵢ/hₒ

⇒ -(-60/-20) = hᵢ/5

⇒ -3 = hᵢ/5

⇒ hᵢ = 5(-3)

⇒ hᵢ = -15 cm

[Negative sign of 'hᵢ' shows that the image is inverted.]

Answer 2

Given :-

for a 5.00-cm tall object placed 20.0 cm from a concave mirror having a focal length of 15.0 cm

To Find :-

Image distance

Image height

Solution :-

We know that

1/u + 1/v = 1/f

1/-20 + 1/v = 1/-15

-1/20 + 1/v = -1/15

1/v = -1/15 + 1/20

1/v = -4 + 3/60

1/v = -1/60

v = -60 cm

Now

m = -v/u = hi/ho

-(-60)/-20 = hi/5

-60/20 = hi/5

5 × (-60) = 20hi

-300 = 20hi

-300/20 = hi

-15 = hi