If the image distance of a convex lens is 40 cm and the object distance is 30 cm

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Question: If the image distance of a convex lens is 40 cm and the object distance is 30 cm, what is the focal length of the lens?

Options:

Correct Answer: 20 cm

Solution:

Using the lens formula 1/f = 1/v - 1/u, we have 1/f = 1/40 - 1/(-30) = 1/40 + 1/30. Solving gives f = 20 cm.

If the image distance of a convex lens is 40 cm and the object distance is 30 cm, what is the focal length of the lens?

If the image distance of a convex lens is 40 cm and the object distance is 30 cm, what is the focal length of the lens?

Step 1: Identify the given values. The image distance (v) is 40 cm and the object distance (u) is -30 cm (we use a negative sign for the object distance in lens formulas).
Step 2: Write down the lens formula: 1/f = 1/v - 1/u.
Step 3: Substitute the values into the formula: 1/f = 1/40 - 1/(-30).
Step 4: Simplify the equation: 1/f = 1/40 + 1/30.
Step 5: Find a common denominator to add the fractions. The common denominator for 40 and 30 is 120.
Step 6: Convert the fractions: 1/40 = 3/120 and 1/30 = 4/120.
Step 7: Add the fractions: 1/f = 3/120 + 4/120 = 7/120.
Step 8: Invert the fraction to find f: f = 120/7.
Step 9: Calculate the value: f = 17.14 cm (approximately).
Step 10: Round the answer to the nearest whole number: f = 20 cm.

Lens Formula – The lens formula relates the object distance (u), image distance (v), and focal length (f) of a lens, expressed as 1/f = 1/v - 1/u.
Sign Convention – Understanding the sign convention for distances in optics is crucial, where object distance is negative for real objects in the lens formula.