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A dense glass double convex lens (n = 2) designed to reduce spherical aberration has |R1| : |R2| = 1:5. If a point object is kept 15 cm in front of this lens, it produces its real image at 7.5 cm. Determine R1 and R2.

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Given: |R1| : |R2| = 1 : 5, u = -15 cm,

v = +7.5 cm, n = 2

To Find: Radii of curvature of double convex lens (R1) and (R2)

Formula:

Calculation: From formula (i),

\(\frac{1}{f}=\frac{1}{7.5}-\frac{1}{(-15)}=\frac{1}{5}\)

∴ f = +5 cm

Substituting this value in formula (ii), we get,

By sign conventions,

Substituting in equation (1),

∴ R1 = 6 cm

Using in equation (2),

R2 = 5 × 6 = 30 cm

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