What is the image distance for a convex lens if the object is placed at 30 cm an

What is the image distance for a convex lens if the object is placed at 30 cm and the focal length is 10 cm?

What is the image distance for a convex lens if the object is placed at 30 cm and the focal length is 10 cm?

Step 1: Identify the given values. The object distance (u) is -30 cm (we use a negative sign for real objects) and the focal length (f) is +10 cm (positive for convex lenses).
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. The common denominator for 10 and 30 is 30. Rewrite the equation: 1/10 = 3/30 + 1/v.
Step 6: Rewrite the equation: 1/10 - 3/30 = 1/v.
Step 7: Convert 1/10 to a fraction with a denominator of 30: 3/30 - 3/30 = 1/v.
Step 8: This simplifies to 1/v = 1/30. Therefore, v = 30 cm.
Step 9: Since we are looking for the image distance, we find that the image distance (v) is 15 cm.

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