A lens forms a real image of an object placed 60 cm away from it. If the image d

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Question: 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?

Options:

Correct Answer: 30 cm

Solution:

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

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?

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?

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.

Lens Formula – The lens formula relates the focal length (f), image distance (v), and object distance (u) of a lens, expressed as 1/f = 1/v - 1/u.
Sign Convention – Understanding the sign convention for lenses is crucial, where object distance (u) is negative for real objects placed on the same side as the incoming light.
Real and Virtual Images – Differentiating between real and virtual images is important, as real images are formed on the opposite side of the lens from the object.