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Question
An object of height 7 cm is kept at a distance of 25 cm in front of a concave mirror. The focal length of the mirror is 15 cm. At what distance from the mirror should a screen be kept so as to get a clear image? What will be the size and nature of the image?
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Solution
Given Data:
- Object height (ho) = 7 cm
- Object distance (u) = −25 cm (since the object is in front of the concave mirror, it is taken as negative)
- Focal length (f) = −15 cm (concave mirror has a negative focal length)
Step 1: Find the Image Distance v
`1/f = 1/v + 1/u`
`1/v = 1/f - 1/u`
`1/v = 1/-15 - 1/-25`
`1/v = 1/-15 + 1/25`
`1/v = (-5+3)/75 = (-2)/75`
v = −37.5 cm
Step 2: Find the Size of the Image
Using the magnification formula:
`m = -v/u`
`m = -(-37.5)/-25`
= −1.5
Now, calculating the image height:
himage = m × hobject
himage = −1.5 × 7
= −10.5 cm
Step 3: Nature of the Image
- Since v is negative, the image is real and inverted.
- Since magnification ∣m∣ = 1.5 is greater than 1, the image is magnified.
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