What is the focal length of a convex lens of focal length 30cm in contact with a concave lens of focal length 20cm? Is the system a converging or a diverging lens? Ignore thickness of the lenses.
The focal length of the combination is -60 cm. The system acts as a diverging lens.
Explanation
When two thin lenses are placed in contact, their combined focal length is determined using the formula: 1/f = 1/f₁ + 1/f₂. For a convex lens, focal length is taken as positive, while for a concave lens, it is taken as negative. The negative sign of the resultant focal length indicates that the combination behaves as a diverging lens.
Solution Steps
Step 1: Identify the focal lengths: Convex lens f₁ = +30 cm, Concave lens f₂ = -20 cm (negative for concave lens).
Step 2: Apply the lens combination formula: 1/f = 1/f₁ + 1/f₂
Step 3: Substitute values: 1/f = 1/30 + 1/(-20) = 1/30 - 1/20
Step 4: Calculate: 1/f = (2 - 3)/60 = -1/60
Step 5: Therefore, f = -60 cm. Since focal length is negative, the system is a diverging lens.