An object is placed at a distance of 40 cm from a concave mirror of a focal length of 15 cm. If the object is

Question

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

Accepted Answer

We use the mirror formula: $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$.

**Case 1 (Initial Position):**
*   Object distance, $u_1 = -40 	ext{ cm}$.
*   Focal length, $f = -15 	ext{ cm}$ (concave mirror).
*   $\frac{1}{v_1} = \frac{1}{f} - \frac{1}{u_1} = \frac{1}{-15} - \frac{1}{-40} = \frac{-8 + 3}{120} = \frac{-5}{120}$.
*   $v_1 = -24 	ext{ cm}$. The initial image is 24 cm in front of the mirror.

**Case 2 (Final Position):**
*   The object is displaced 20 cm *towards* the mirror. New object distance $u_2 = -(40 - 20) = -20 	ext{ cm}$.
*   $\frac{1}{v_2} = \frac{1}{f} - \frac{1}{u_2} = \frac{1}{-15} - \frac{1}{-20} = \frac{-4 + 3}{60} = \frac{-1}{60}$.
*   $v_2 = -60 	ext{ cm}$. The new image is 60 cm in front of the mirror.

**Displacement:**
*   Displacement = $|v_2| - |v_1| = 60 - 24 = 36 	ext{ cm}$.
*   Since the image distance increased from 24 cm to 60 cm, the image moved **away** from the mirror.

Thus, the displacement is 36 cm away from the mirror.

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