A concave lens has a focal length of -12 cm. What is the image distance when the

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

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

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 (we use a negative sign for the object distance in lens formulas).
Step 2: Write down the lens formula: 1/f = 1/v - 1/u.
Step 3: Substitute the known values into the lens formula: 1/(-12) = 1/v - 1/(-24).
Step 4: Simplify the equation: 1/(-12) = 1/v + 1/24.
Step 5: To combine the fractions, find a common denominator. The common denominator for 12 and 24 is 24.
Step 6: Rewrite 1/(-12) as -2/24: -2/24 = 1/v + 1/24.
Step 7: Move 1/24 to the left side: -2/24 - 1/24 = 1/v.
Step 8: Combine the fractions on the left side: -3/24 = 1/v.
Step 9: Simplify -3/24 to -1/8: -1/8 = 1/v.
Step 10: Take the reciprocal of both sides to find v: v = -8 cm.

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