Published by:
CGP EDU Academic Team
Published on: September 12, 2026
A linear object AB is placed inclined to the principal axis at an angle 60° in front of concave mirror of R = 20 cm as shown in figure. Find angle made by image A'B' with principal axis.

Text Solution
Verified by ExpertsThe correct answer is:
B
Step 1: First, we need to determine the focal length of the concave mirror. Given the radius of curvature (R) is 20 cm, the focal length (f) is given by the formula:
$$ f = \frac{R}{2} = \frac{20}{2} = 10 \text{ cm} $$
Step 2: The object AB is inclined at 60° to the principal axis. The image A'B' will also be inclined at an angle. According to the mirror formula:
$$ \frac{1}{f} = \frac{1}{u} + \frac{1}{v} $$
where 'u' is the object distance (which we'll consider to be negative since the object is in front of the mirror) and 'v' is the image distance.
Step 3: If the object is placed at a distance 'u', the angles at which the rays hit the mirror will determine the approximate angles of the image. The image will be inverted, and thus the angle of image A'B' will be:
$$ \text{Angle of image A'B'} = 180° - \text{angle of object AB} = 180° - 60° = 120° $$
Step 4: Therefore, the angle made by image A'B' with the principal axis is:
$$ 120° - 90° = 30° $$
Thus, the angle with respect to the principal axis is 30°.
Final Calculation: Since we derived that the angle A'B' with respect to the principal axis is 30°, we can conclude that the image is clearly at this angle. Therefore, the answer is:
Therefore, the correct angle made by image A'B' with the principal axis is 30°, or in the context of the options, B.
$$ f = \frac{R}{2} = \frac{20}{2} = 10 \text{ cm} $$
Step 2: The object AB is inclined at 60° to the principal axis. The image A'B' will also be inclined at an angle. According to the mirror formula:
$$ \frac{1}{f} = \frac{1}{u} + \frac{1}{v} $$
where 'u' is the object distance (which we'll consider to be negative since the object is in front of the mirror) and 'v' is the image distance.
Step 3: If the object is placed at a distance 'u', the angles at which the rays hit the mirror will determine the approximate angles of the image. The image will be inverted, and thus the angle of image A'B' will be:
$$ \text{Angle of image A'B'} = 180° - \text{angle of object AB} = 180° - 60° = 120° $$
Step 4: Therefore, the angle made by image A'B' with the principal axis is:
$$ 120° - 90° = 30° $$
Thus, the angle with respect to the principal axis is 30°.
Final Calculation: Since we derived that the angle A'B' with respect to the principal axis is 30°, we can conclude that the image is clearly at this angle. Therefore, the answer is:
Therefore, the correct angle made by image A'B' with the principal axis is 30°, or in the context of the options, B.
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