Final answer:
The focal length of a double concave lens with refractive index 1.5 and radii of curvature R1 = 30 cm and R2 = 60 cm is -120 cm. The negative sign indicates that the lens is concave.
Step-by-step explanation:
To find the focal length of a double concave lens made of a material with a refractive index of 1.5, you would use the lens maker's equation. This equation relates the focal length of the lens to its radii of curvature and its refractive index. For a double concave lens with radii R1 = 30 cm and R2 = 60 cm, the radii must be used with proper signs according to the sign convention, which typically means they will both be negative because they are concave surfaces.
The lens maker's equation is given by:
1/f = (n - 1) (1/R1 - 1/R2)
Plugging the values into the equation:
1/f = (1.5 - 1) (1/(-30) - 1/(-60))
The arithmetic gives us:
1/f = 0.5 (1/-30 + 1/60) = 0.5 (-2 + 1)/60 = -0.5/60 = -1/120
Thus the reciprocal of the focal length is -1/120, which when inverted gives us:
f = -120 cm
The negative sign indicates that the focal length is on the same side as the incoming light, which is characteristic of a concave lens.