A concave lens has a focal length 15 cm. If the object is placed at 30 cm from the lens, what is the image distance?
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A.
-20 cm
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B.
-10 cm
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C.
-15 cm
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D.
-18 cm
Correct Answer:
B. -10 cm
Explanation:
To calculate the image distance for a concave lens, we use the lens formula: 1/f = 1/v - 1/u.1. Identify the given values using the sign convention: - The focal length (f) for a concave lens is always negative, so f = -15 cm.
- The object distance (u) is measured against the direction of incident light, making it negative, so u = -30 cm.2. Plug the values into the lens formula:
1/(-15) = 1/v - 1/(-30)
3. Simplify the equation:
\-1/15 = 1/v + 1/30
4. Isolate 1/v:
1/v = -1/15 - 1/30
5. Find a common denominator (30) to solve:
1/v = -2/30 - 1/30
1/v = -3/30
1/v = -1/10
6. Solve for v:
v = -10 cmThe negative sign indicates that the image is virtual and formed on the same side of the lens as the object. Therefore, the image distance is -10 cm.
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