What is the image distance for a concave lens with a focal length of -12 cm when the object is placed at 24 cm?

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Q: What is the image distance for a concave lens with a focal length of -12 cm when the object is placed at 24 cm?

Solution: Using the lens formula, 1/f = 1/v - 1/u, we find v = -8 cm.

Steps: 9

Step 1: Identify the given values. The focal length (f) of the concave lens is -12 cm, and the object distance (u) is 24 cm.
Step 2: Write down the lens formula: 1/f = 1/v - 1/u.
Step 3: Substitute the known values into the lens formula. Replace f with -12 cm and u with -24 cm: 1/(-12) = 1/v - 1/24.
Step 4: Simplify the equation. This gives: -1/12 = 1/v - 1/24.
Step 5: To isolate 1/v, add 1/24 to both sides: 1/v = -1/12 + 1/24.
Step 6: Find a common denominator to combine the fractions. The common denominator for 12 and 24 is 24.
Step 7: Rewrite -1/12 as -2/24. Now the equation is: 1/v = -2/24 + 1/24.
Step 8: Combine the fractions: 1/v = -2/24 + 1/24 = -1/24.
Step 9: Take the reciprocal to find v: v = -24 cm.