9.1 A small candle, 2.5 cm in size is placed at 27 cm in front of a concave mirror of radius of curvature 36 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved?
Hint: Use mirror formula.
Step 1: Draw a diagram.
Step 2: Find the focal length of the mirror.
The radius of curvature of the concave mirror, R= - 36 cm
The focal length of the concave mirror, f = = − 18 cm
Step 3: Find the image distance.
Object distance, u = - 27 cm
Let the image distance = v
Using the mirror formula:
\(\Rightarrow \frac{1}{v}=\frac{1}{f}-\frac{1}{u}=-\frac{1}{18}+\frac{1}{27}=\frac{1}{54}\)
or, v = -54 cm
The screen should be placed 54 cm away from the mirror to obtain a sharp image.
Step 4: Find the magnification of the image.
Step 5: Find the height of the image
Height of the image = m×Height of the object
= -2×2.5 cm
= - 5 cm
The height of the candle's image is 5 cm. The negative sign indicates that the image is inverted and real.
If the candle is moved closer to the mirror, the picture must be obtained by moving the screen away from the mirror.
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