If a concave lens has a focal length of -10 cm, what is the nature of the image formed when the object is placed at 5 cm?

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Q: If a concave lens has a focal length of -10 cm, what is the nature of the image formed when the object is placed at 5 cm?

Solution: Concave lenses always produce virtual and upright images.

Steps: 10

Step 1: Understand that a concave lens has a negative focal length. In this case, the focal length is -10 cm.
Step 2: Know that when using a lens, the object distance (u) is considered negative if the object is on the same side as the incoming light. Here, the object is at 5 cm, so u = -5 cm.
Step 3: Use the lens formula: 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance.
Step 4: Substitute the values into the lens formula: 1/(-10) = 1/v + 1/(-5).
Step 5: Simplify the equation: -1/10 = 1/v - 1/5.
Step 6: Find a common denominator and solve for 1/v: -1/10 + 1/5 = 1/v.
Step 7: Calculate 1/5 as 2/10, so -1/10 + 2/10 = 1/10. Therefore, 1/v = 1/10.
Step 8: Invert to find v: v = 10 cm.
Step 9: Since v is positive, it indicates that the image is formed on the same side as the object, which means it is virtual.
Step 10: Remember that concave lenses always produce virtual and upright images.