Question

An object is placed 15cm from a converging mirror of radius of curvature 20cm .Calculate the image position and magnification.

Answer 1

Hola mate! Here is your answer:

Given:

Concave mirror

u=(-15cm)

f = -10cm

Solution:

Using mirror formula

$\frac{1}{f} = \frac{1}{v} </em><em>+</em><em> \frac{1}{u}$

$\frac{1}{v} = \frac{1}{</em><em>-</em><em>10} </em><em>+</em><em> \frac{1}{15}$

$\frac{1}{v} = \frac{</em><em>-</em><em>5</em><em>}{150}$

$v = </em><em>-</em><em>3</em><em>0</em><em>cm$

Using magnification formula:

$\frac{</em><em>-</em><em>v}{u} = m \\ \frac{</em><em>-</em><em>(</em><em>-</em><em>3</em><em>0</em><em>)</em><em>}{ - 15} = m$

m=-2

Thus image is Real and Inverted and is Magnified

Answer 2

Explanation:

) u = -15cm,

R = -20cm (Converging mirror)

f = R/2 = -10 cm

1/v + 1/u = 1/f

1/v + 1/-15 = 1/-10

⇒ 1/v – 1/15 = -(1/10)

⇒ 1/v = 1/15 – 1/10 = (2 -3)/30 = - (1/30)

∴ v = - 30 cm

The image is formed 30 cm in front of the mirror.

m = - (v/u) = - (-30)/(-15) = -2

(b) u = -15cm,

R = 20cm (Diverging mirror)

f = R/2 = 10 cm

1/v + 1/u = 1/f

1/v + 1/-15 = 1/10

⇒ 1/v – 1/15 = 1/10

⇒ 1/v = 1/15 + 1/10 = (2 + 3)/30 = 5/30

∴ v = 6 cm

The image is formed 6 cm behind the mirror.

m = - (v/u) = - (6)/(-15) = 0.4