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A microscope objective collects light within a cone of half-angle 30 deg and is used with visible light of wavelength 5500 Angstrom. Estimate its limit of resolution.

1. 2.5 * 10⁻⁵ cm
2. 4.6 * 10⁻⁵ cm
3. 3.9 * 10⁻⁵ cm
4. 6.7 * 10⁻⁵ cm

Correct answer: 6.7 * 10⁻⁵ cm

Solution

The limit of resolution of a microscope is d_min = 1.22*lambda/(2*n*sin(theta)). With n = 1 and theta = 30 deg, 2*sin(30) = 2*0.5 = 1, so d_min = 1.22*lambda = 1.22*5500*10⁻⁸ cm = 1.22*5.5*10⁻⁵ = 6.71*10⁻⁵ cm.

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