A convex lens has a focal length of 20 cm. If an object is placed 60 cm from the lens, what is the distance of the image from the lens?

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Q: A convex lens has a focal length of 20 cm. If an object is placed 60 cm from the lens, what is the distance of the image from the lens?

Solution: Using the lens formula 1/f = 1/v - 1/u, we find v = 30 cm.

Steps: 9

Step 1: Identify the given values. The focal length (f) of the lens is 20 cm, and the object distance (u) is 60 cm.
Step 2: Use the lens formula, which is 1/f = 1/v - 1/u.
Step 3: Substitute the known values into the lens formula. This gives us 1/20 = 1/v - 1/60.
Step 4: Rearrange the equation to solve for 1/v. This means 1/v = 1/20 + 1/60.
Step 5: Find a common denominator to add the fractions. The common denominator for 20 and 60 is 60.
Step 6: Rewrite 1/20 as 3/60. Now the equation is 1/v = 3/60 + 1/60.
Step 7: Add the fractions: 3/60 + 1/60 = 4/60.
Step 8: Now, we have 1/v = 4/60. To find v, take the reciprocal: v = 60/4.
Step 9: Calculate 60/4, which equals 15 cm. Therefore, the distance of the image from the lens is 15 cm.