The focal length of a thin lens made from the material of refractive index 1.5 is 20 cm. When it is placed in a liquid of refractive index 1.33, its focal length will be cm.

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(4) 78.23. Given: lens glass n=1.5, focal length in air f=20 cm, liquid nₗ=1.33. Idea: in the lens maker's formula only the term (n-1) changes when the surroundings change — the shape factor K=1/(R₁)-1/(R₂) belongs to the glass and stays the same. In a medium, (n-1) becomes (n/(nₗ)-1). In air: 1/(20)=(1.5-1)K, so K=1/(10) cm⁻¹. In the liquid the relative index is (1.5)/(1.33)=1.1278, so 1/(f')=(1.1278-1)×1/(10)=0.01278 cm⁻¹. So f'=78.23 cm. The lens is about four times weaker in the liquid, because the jump in refractive index at its surface is about four times smaller.

The focal length of a thin lens made from the material of refractive index 1.5 is 20 cm. When it is placed in a liquid of refractive index 1.33, its focal length will be ______ cm.

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