Question:
A rod of length 10 cm lies along the principle axis of a concave mirror of focal length 10 cm as shown in figure. The length of the image is ______ cm.
A rod of length 10 cm lies along the principle axis of a concave mirror of focal length 10 cm as shown in figure. The length of the image is ______ cm.
Updated On: Apr 10, 2026
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
When an object (rod) lies along the principal axis, we find the positions of the images of its two endpoints using the mirror formula. The length of the image is the distance between these two image points.
Step 2: Key Formula or Approach:
1. Mirror Formula: $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$. 2. Focal length $f = -10$ cm (concave mirror). 3. Identify $u_1$ and $u_2$ for the two ends of the rod.
Step 3: Detailed Explanation:
1. Let the rod be placed such that one end is at $20$ cm ($2f$, the center of curvature $C$) and the other end is further away at $30$ cm. 2. For End 1 ($u_1 = -20$ cm): Since the object is at $C$, the image is also at $C$ ($v_1 = -20$ cm). 3. For End 2 ($u_2 = -30$ cm): $\frac{1}{v_2} + \frac{1}{-30} = \frac{1}{-10} \implies \frac{1}{v_2} = \frac{1}{30} - \frac{1}{10} = \frac{1-3}{30} = -\frac{2}{30}$. $v_2 = -15$ cm. 4. Length of Image $= |v_1 - v_2| = |-20 - (-15)| = 5$ cm.
Step 4: Final Answer:
The length of the image is 5 cm.
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