What is the focal length of a diverging lens if the image distance is -15 cm and

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Question: What is the focal length of a diverging lens if the image distance is -15 cm and the object distance is -10 cm? (2023)

Options:

Correct Answer: -20 cm

Exam Year: 2023

Solution:

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

What is the focal length of a diverging lens if the image distance is -15 cm and the object distance is -10 cm? (2023)

What is the focal length of a diverging lens if the image distance is -15 cm and the object distance is -10 cm? (2023)

Step 1: Identify the given values. The image distance (v) is -15 cm and the object distance (u) is -10 cm.
Step 2: Write down the lens formula: 1/f = 1/v - 1/u.
Step 3: Substitute the values into the lens formula. Replace v with -15 cm and u with -10 cm: 1/f = 1/(-15) - 1/(-10).
Step 4: Calculate 1/(-15) which is -1/15 and 1/(-10) which is -1/10.
Step 5: Now, calculate -1/15 - (-1/10). This is the same as -1/15 + 1/10.
Step 6: Find a common denominator for 15 and 10, which is 30. Rewrite the fractions: -1/15 = -2/30 and 1/10 = 3/30.
Step 7: Now add the fractions: -2/30 + 3/30 = 1/30.
Step 8: So, we have 1/f = 1/30. To find f, take the reciprocal: f = 30 cm.
Step 9: Since this is a diverging lens, the focal length is negative. Therefore, f = -30 cm.

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