An object is placed 15 cm in front of a convex lens of focal length 10 cm. What

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Question: An object is placed 15 cm in front of a convex lens of focal length 10 cm. What is the position of the image formed? (2020)

Options:

Correct Answer: 30 cm

Exam Year: 2020

Solution:

Using the lens formula: 1/f = 1/v - 1/u, where f = 10 cm and u = -15 cm, we find v = 30 cm.

An object is placed 15 cm in front of a convex lens of focal length 10 cm. What is the position of the image formed? (2020)

An object is placed 15 cm in front of a convex lens of focal length 10 cm. What is the position of the image formed? (2020)

Step 1: Identify the given values. The focal length (f) of the convex lens is 10 cm, and the object distance (u) is 15 cm.
Step 2: Use the lens formula: 1/f = 1/v - 1/u. Here, f is the focal length, v is the image distance, and u is the object distance.
Step 3: Substitute the values into the lens formula. Since the object distance is in front of the lens, we take u as -15 cm. So, the formula becomes: 1/10 = 1/v - 1/(-15).
Step 4: Simplify the equation. This gives us: 1/10 = 1/v + 1/15.
Step 5: Find a common denominator for the right side. The common denominator for 10 and 15 is 30. Rewrite the equation: 1/10 = 3/30 + 2/30 = (3 + 2)/30 = 5/30.
Step 6: Set the left side equal to the right side: 1/10 = 5/30. Cross-multiply to solve for v: 30 = 5v.
Step 7: Divide both sides by 5 to find v: v = 30 cm.

Lens Formula – The lens formula relates the focal length (f), object distance (u), and image distance (v) for a lens, expressed as 1/f = 1/v - 1/u.
Convex Lens Properties – A convex lens converges light rays and can produce real and inverted images when the object is placed outside the focal length.
Sign Convention – Understanding the sign convention for distances in optics is crucial, where object distance (u) is negative for real objects placed in front of the lens.