A concave lens has a focal length of 25 cm. What is the image distance when the

A concave lens has a focal length of 25 cm. What is the image distance when the object is placed at 50 cm?

A concave lens has a focal length of 25 cm. What is the image distance when the object is placed at 50 cm?

Step 1: Understand the lens formula, which is 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance.
Step 2: Identify the values given in the problem. The focal length (f) of the concave lens is -25 cm (negative because it's a concave lens) and the object distance (u) is -50 cm (negative because the object is on the same side as the incoming light).
Step 3: Substitute the values into the lens formula: 1/(-25) = 1/v + 1/(-50).
Step 4: Simplify the equation: 1/v = 1/(-25) + 1/50.
Step 5: Find a common denominator to combine the fractions: 1/v = -2/50 + 1/50 = -1/50.
Step 6: Invert the fraction to find v: v = -50 cm.

Lens Formula – The lens formula relates the object distance (u), image distance (v), and focal length (f) of a lens: 1/f = 1/v + 1/u.
Concave Lens Properties – Concave lenses always produce virtual images that are upright and reduced in size, with a negative image distance.