Question

An object is placed at a distance of 40 cm from a concave mirror of focal length 15 cm. If the object is displaced through a distance of 20 cm towards the mirror, the displacement of the image will be

• A. 30 cm away from the mirror
• B. 30 cm towards the mirror
• C. 36 cm away from the mirror
• D. 36 cm towards the mirror

Answer 1

The Correct Option is C

To solve this problem, analyze the change in image position for a concave mirror.

Given:

• \( u_1 = -40\,\text{cm} \)
• \( f = -15\,\text{cm} \)
• \( u_2 = -20\,\text{cm} \)

Mirror formula:

\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]

Initial image position:

\[ \frac{1}{-15} = \frac{1}{v_1} - \frac{1}{40} \]

\[ \frac{1}{v_1} = \frac{1}{-15} + \frac{1}{40} = \frac{-40 + 15}{600} = -\frac{1}{24} \]

\[ v_1 = -24\,\text{cm} \]

Final image position:

\[ \frac{1}{-15} = \frac{1}{v_2} - \frac{1}{20} \]

\[ \frac{1}{v_2} = \frac{1}{-15} + \frac{1}{20} = \frac{-20 + 15}{300} = -\frac{1}{60} \]

\[ v_2 = -60\,\text{cm} \]

Displacement of image:

\[ \Delta v = v_2 - v_1 = -60 - (-24) = -36\,\text{cm} \]

The negative sign indicates the image moves away from the mirror.

Final Answer: \( 36\,\text{cm} \) away from the mirror