Refraction At Spherical Surfaces And By Lenses

Step 1: Recall the lens maker's formula.

The lens maker's formula for a thin lens is:

where:

• is the focal length,
• is the refractive index of the lens material,
• and are the radii of curvature of the two surfaces.

Step 2: Substitute the given values.

For a double concave lens:

• (negative because the surface is concave),
• (positive because the surface is concave),
• .

Substitute into the formula:

Simplify:

Find a common denominator for the fractions:

Substitute back:

Invert to find :

Final Answer: The focal length is , which corresponds to option .