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Chapter 4: Problem 70

If a microscope can accept light from objects at angles as large as \(\alpha=70^{\circ},\) what is the smallest structure that can be resolved when illuminated with light of wavelength 500 nm and (a) the specimen is in air? (b) When the specimen is immersed in oil, with index of refraction of \(1.52 ?\)

Short Answer

Expert verified
The smallest structure that can be resolved when the specimen is in air will be approximately \(4.06 \times 10^{-7} m\) and when the specimen is immersed in oil will be approximately \(2.67 \times 10^{-7} m\).

Step by step solution

01

Resolve in Air

Using the formula \(d = \lambda / (2 \cdot \sin(\alpha))\), we can substitute the given values: \(d = 500 \times 10^{-9} m / (2 \cdot \sin(70^{\circ}))\) to find the smallest structure that can be resolved in air.
02

Resolve in Oil

When the specimen is immersed in oil, the index of refraction needs to be taken into account. This alters the formula to \(d = \lambda / (2 \cdot n \cdot \sin(\alpha))\), where \(n\) is the index of refraction. Substitute the given values: \(d = 500 \times 10^{-9} m / (2 \cdot 1.52 \cdot \sin(70^{\circ})\) to find the smallest structure that can be resolved in oil.

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Most popular questions from this chapter

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