What is the image distance for a convex lens with a focal length of 10 cm when t

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Question: What is the image distance for a convex lens with a focal length of 10 cm when the object is placed 30 cm from the lens?

Options:

Correct Answer: 20 cm

Solution:

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

What is the image distance for a convex lens with a focal length of 10 cm when the object is placed 30 cm from the lens?

What is the image distance for a convex lens with a focal length of 10 cm when the object is placed 30 cm from the lens?

Step 1: Identify the given values. The focal length (f) of the convex lens is 10 cm, and the object distance (u) is -30 cm (we use a negative sign for object distance in lens formulas).
Step 2: Write down the lens formula: 1/f = 1/v - 1/u.
Step 3: Substitute the known values into the lens formula: 1/10 = 1/v - 1/(-30).
Step 4: Simplify the equation: 1/10 = 1/v + 1/30.
Step 5: Find a common denominator for the right side of the equation. The common denominator for 10 and 30 is 30.
Step 6: Rewrite the equation: 1/10 = 3/30 + 1/v.
Step 7: Rearrange the equation to isolate 1/v: 1/v = 1/10 - 3/30.
Step 8: Convert 1/10 to have a denominator of 30: 1/10 = 3/30, so 1/v = 3/30 - 3/30 = 0.
Step 9: Since 1/v = 0, this means v is infinite, which indicates that the image is formed at infinity.

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