Question:
When an object is placed 40 cm away from a spherical mirror an image of magnification $\frac{1}{2}$ is produced. To obtain an image with magnification of $\frac{1}{3}$, the object is to be moved:
When an object is placed 40 cm away from a spherical mirror an image of magnification $\frac{1}{2}$ is produced. To obtain an image with magnification of $\frac{1}{3}$, the object is to be moved:
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Use the magnification formula to find the object distance.
Updated On: Apr 25, 2025
- 40 cm away from the mirror.
- 80 cm away from the mirror.
- 20 cm towards the mirror.
- 20 cm away from the mirror.
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The Correct Option is A
Solution and Explanation
1. Given:
- Object distance, $u = -40 \mathrm{~cm}$
- Magnification, $m = \frac{1}{2}$
2. Magnification formula: \[ m = \frac{f}{f - u} \] \[ \frac{1}{2} = \frac{f}{f - (-40)} \] \[ f + 40 = 2f \implies f = 40 \mathrm{~cm} \]
3. For magnification $\frac{1}{3}$: \[ \frac{1}{3} = \frac{40}{40 - u} \] \[ 40 - u = 120 \implies u = -80 \mathrm{~cm} \] Therefore, the correct answer is (1) 40 cm away from the mirror.
2. Magnification formula: \[ m = \frac{f}{f - u} \] \[ \frac{1}{2} = \frac{f}{f - (-40)} \] \[ f + 40 = 2f \implies f = 40 \mathrm{~cm} \]
3. For magnification $\frac{1}{3}$: \[ \frac{1}{3} = \frac{40}{40 - u} \] \[ 40 - u = 120 \implies u = -80 \mathrm{~cm} \] Therefore, the correct answer is (1) 40 cm away from the mirror.
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