An object is placed at a distance of 30 cm from a convex lens of focal length 15

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Question: An object is placed at a distance of 30 cm from a convex lens of focal length 15 cm. What is the distance of the image from the lens?

Options:

Correct Answer: 20 cm

Solution:

Using the lens formula, 1/f = 1/v - 1/u. Here, f = 15 cm, u = -30 cm. Solving gives v = 10 cm.

An object is placed at a distance of 30 cm from a convex lens of focal length 15 cm. What is the distance of the image from the lens?

An object is placed at a distance of 30 cm from a convex lens of focal length 15 cm. What is the distance of the image from the lens?

Step 1: Identify the given values. The focal length (f) of the convex lens is 15 cm, and the object distance (u) is 30 cm.
Step 2: Remember that in lens formulas, the object distance (u) is taken as negative. So, u = -30 cm.
Step 3: Write down the lens formula: 1/f = 1/v - 1/u.
Step 4: Substitute the known values into the lens formula: 1/15 = 1/v - 1/(-30).
Step 5: Simplify the equation: 1/15 = 1/v + 1/30.
Step 6: Find a common denominator for the right side of the equation. The common denominator for 15 and 30 is 30.
Step 7: Rewrite the equation: 1/15 = 2/60 + 1/v.
Step 8: Convert 1/15 to have a denominator of 60: 1/15 = 4/60.
Step 9: Now the equation is: 4/60 = 2/60 + 1/v.
Step 10: Subtract 2/60 from both sides: 4/60 - 2/60 = 1/v.
Step 11: This simplifies to: 2/60 = 1/v.
Step 12: Invert both sides to find v: v = 60/2.
Step 13: Calculate v: v = 30 cm.

Lens Formula – The lens formula relates the focal length (f), object distance (u), and image distance (v) of a lens, expressed as 1/f = 1/v - 1/u.
Sign Convention – Understanding the sign convention for distances in optics, where object distance (u) is negative for real objects placed on the same side as the incoming light.
Convex Lens Properties – A convex lens converges light rays and can produce real or virtual images depending on the position of the object relative to the focal length.