Question

If a microscope can accept light from objects at angles as large as α=70°, 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?

Answer 1

The smallest structure that can be resolved by a microscope under light with a wavelength of 500 nm depends on the medium between the lens and specimen. Using the formula ∆y = λ / (2NA) and calculating the Numerical Aperture (NA) for air and oil immersions, we can determine the resolution limit for each scenario.

Step-by-step explanation:

The student is asking about the resolution limit of a microscope when a specimen is illuminated with 500 nm wavelength light in different conditions. The resolution limit is given by the equation ∆y = λ / (2NA), where NA (Numerical Aperture) is given by NA = n*sin(α), with α being the maximum acceptance angle and n is the refractive index of the medium between the objective lens and the specimen. The smallest structure that can be resolved:

• (a) In air (n = 1.00), NA = 1.00 * sin(70°), which gives a maximum resolution of ∆y.
• (b) In oil (n = 1.52), NA = 1.52 * sin(70°), which gives a maximum resolution of ∆y.

To find the values of ∆y, one would calculate each NA using n values for air and oil and then apply the equation ∆y = 500 nm / (2NA) for both cases to find the smallest resolvable structure.