Question

a concave mirror of radius of curvature 30 cm produces a real image 3 times the size of the object. The distance between the object and the image i​

Answer 1

Given : A concave mirror of radius of curvature 30cm produces a real image three times the size of the object.

To find : The distance between object and image.

solution : radius of curvature of concave mirror, R = 30cm

so, focal length of concave mirror, f = -R/2 = -15 cm

as a real image three times the size of the object.

magnification, m = - 3 [ negative sign indicates image is real]

⇒-v/u = -3

⇒v = 3u ......(1)

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

⇒1/3u + 1/u = 1/-15

⇒4/3u = 1/-15

⇒u = - 20 cm

v = 3u = 3 × -20 = -60cm

Therefore the distance between the object and the image (60cm - 20cm) = 40cm.

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Answer 2

Distance between object and image = 40 cm

Explanation:

Given: A concave mirror of radius of curvature 30cm produces a real image three times the size of the object.

Find: Distance between Object and image.

Solution: R = 30 cm

Focal length of the concave mirror f = -R/2 = -15 cm

m = v / u = 3

So v = 3u --------------(1)

Using mirror formula:

1/f = 1/v + 1/u

1/-15 = 1/3u + 1/u

 -1/15 = 4/ 3u

 -3u = 4 * 15

 -u = 4*15/3

 u = -20 cm

So v = 3u = 3 * -20 = -60 cm

Distance between object and image = 60 - 20 = 40 cm