A 1 cm object is placed perpendicular to the principal axis of a convex mirror of focal length 7.5 cm . Determine its distance from the mirror if the resulting image is 0.6 cm in size.

Correct answer: B. 5 cm Given h_ o = 1 cm , f = +7.5 cm , and h_ i = +0.6 cm (virtual and erect image for a convex mirror). Magnification m = h_ i h_ o = (0.6)/(1) = 0.6 Using m = -(v)/(u) , we get v = -0.6u . Applying the mirror formula: (1)/(v) + (1)/(u) = (1)/(f) (1)/(-0.6u) + (1)/(u) = (1)/(7.5) (-1 + 0.6)/(0.6u) = (1)/(7.5) (-0.4)/(0.6u) = (1)/(7.5) (-2)/(3u) = (1)/(7.5) 3u = -15 u = -5 cm The distance of the object from the mirror is 5 cm .

Concepts Of Physics MCQ Edition [Volume 1]

Exam: Concepts Of Physics MCQ Edition [Volume 1]
Subject: Physics
Chapter: Geometrical Optics

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Geometrical Optics

A 1 cm object is placed perpendicular to the principal axis of a...

1 \text{ cm}

object is placed perpendicular to the principal axis of a convex mirror of focal length

7.5 \text{ cm}

. Determine its distance from the mirror if the resulting image is

0.6 \text{ cm}

in size.

Options

A $7.5 \text{ cm}$
B $5 \text{ cm}$
C $2.5 \text{ cm}$
D $10 \text{ cm}$

Correct answer

B. $5 \text{ cm}$

Step-by-step solution

Given

h_{o} = 1 \text{ cm}

f = +7.5 \text{ cm}

, and

h_{i} = +0.6 \text{ cm}

(virtual and erect image for a convex mirror).

Magnification

m = \dfrac{h_{i}}{h_{o}} = \dfrac{0.6}{1} = 0.6

Using

m = -\dfrac{v}{u}

, we get

v = -0.6u

.

Applying the mirror formula:

\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}

\dfrac{1}{-0.6u} + \dfrac{1}{u} = \dfrac{1}{7.5}

\dfrac{-1 + 0.6}{0.6u} = \dfrac{1}{7.5}

\dfrac{-0.4}{0.6u} = \dfrac{1}{7.5}

\dfrac{-2}{3u} = \dfrac{1}{7.5}

3u = -15 \Rightarrow u = -5 \text{ cm}

The distance of the object from the mirror is

5 \text{ cm}

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