Should the antireflection coating of a microscope objective lens designed for use with ultraviolet light be thinner, thicker, or the same thickness as the coating on a lens designed for visible light?

the thickness to meet the equation must be less than in a system for visible Liz t _UV < t_visible

Explanation:

When a ray enters the film antireflector that generally has a refractive index greater than the glass index, it experiences a phase change of 180, similar to when we have a collision with a wall.

When the beam reaches the bottom of the film-glass interface film, the refractive impact of the film is greater than that of the glass, it does not experience any change in phase.

Within the film the beam experiences a change in its propagation speed, the frequency in the air and the film is the same, since the propagation of a resonant type process, to fulfill the equation

v = λₙ f

The wavelength must change c = λ₀ f

c / v = λ₀ / λₙ

n = λ₀ / λₙ

λₙ = λ₀ / n

In general this type of reflection is almost normal to the surface, so we can calculate the optical path difference, if t is the thickness of the film, for constructive interference

2t = m λₙ + λₙ / 2

2t = (m + ½) λₙ

This is the condition to see a bright beam.], For destructive interference the equation is

2t = m λₙ

t = m λₙ / 2

Since the wavelength of visible light 400 to 700 is not much male than the wavelength of ultra violet light Lam <400 no, the thickness to meet the equation must be less than in a system for visible Liz

t _UV < t_visible