Concept: The Lens Maker’s Formula relates the focal length of a lens to:
Refractive index of lens material
Radii of curvature of its two surfaces
It is derived using refraction at two spherical surfaces.
Assumptions:
Thin convex lens
Refractive index of lens =
Lens in air ( )
Radii of curvature = and
Step 1: Refraction at first spherical surface Using refraction formula at a spherical surface: For first surface:
Light travels from air to glass
Object at distance , image formed at
Step 2: Refraction at second spherical surface Now the image formed by the first surface acts as the object for the second surface. For second surface:
Light travels from glass to air
Object distance =
Final image distance =
Step 3: Add equations (1) and (2) Cancel : Step 4: For focal length For focal length, object at infinity: Lens Maker’s Formula: Notes:
Valid for thin lenses.
Sign convention must be used carefully.
For convex lens in air, , .