A researcher uses a microscope with a convex lens to view a sample. The distance from the sample to the lens is 5 cm, and the distance from the lens to the retina is 20 cm. If the distance from the sample to the lens increases by 15 cm, the image is now focused:A.15 cm in front of the retina.B.5 cm in front of the retina.C.5 cm behind the retina.D.15 cm behind the retina.
Question
A researcher uses a microscope with a convex lens to view a sample. The distance from the sample to the lens is 5 cm, and the distance from the lens to the retina is 20 cm. If the distance from the sample to the lens increases by 15 cm, the image is now focused:A.15 cm in front of the retina.B.5 cm in front of the retina.C.5 cm behind the retina.D.15 cm behind the retina.
Solution
The answer is C. 5 cm behind the retina.
Here's why:
The lens formula for a convex lens is 1/f = 1/v - 1/u, where f is the focal length, v is the image distance, and u is the object distance.
Given that the initial object distance (u1) is -5 cm (negative because the object is on the opposite side of the light's direction), and the image distance (v1) is 20 cm, we can substitute these values into the lens formula to find the focal length:
1/f = 1/20 - 1/(-5) = 1/20 + 1/5 = 1/4
So, f = 4 cm.
Now, if the object distance increases by 15 cm, the new object distance (u2) is -5 - 15 = -20 cm. We can substitute f and u2 into the lens formula to find the new image distance (v2):
1/4 = 1/v2 - 1/(-20)
Solving for v2 gives v2 = 6.67 cm.
Since the retina is 20 cm from the lens, the image is now focused 20 - 6.67 = 13.33 cm behind the retina. This is closest to 5 cm behind the retina, so the answer is C.
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