A lens forms a real image of an object placed 60 cm away from it. If the image distance is 20 cm, what is the focal length of the lens?

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Q: A lens forms a real image of an object placed 60 cm away from it. If the image distance is 20 cm, what is the focal length of the lens?

Solution: Using the lens formula 1/f = 1/v - 1/u, where u = -60 cm and v = 20 cm, we find f = 30 cm.

Steps: 10

Step 1: Identify the given values. The object distance (u) is 60 cm and the image distance (v) is 20 cm.
Step 2: Remember that in lens formulas, the object distance (u) is taken as negative. So, u = -60 cm.
Step 3: Write down the lens formula: 1/f = 1/v - 1/u.
Step 4: Substitute the values into the formula. We have v = 20 cm and u = -60 cm.
Step 5: Calculate 1/v. This is 1/20 cm = 0.05.
Step 6: Calculate 1/u. This is 1/(-60 cm) = -1/60 cm = -0.01667.
Step 7: Now substitute these values into the lens formula: 1/f = 0.05 - (-0.01667).
Step 8: Simplify the right side: 1/f = 0.05 + 0.01667 = 0.06667.
Step 9: To find f, take the reciprocal: f = 1/0.06667.
Step 10: Calculate f, which gives you approximately 15 cm.