Question

A microscope has a 1 cm diameter objective lens with a focal length of 2.8 mm. The microscope is using light with a wavelength of 550 nm

a. What color is the light?

b. What is the resolving power of the objective if used in air?

c. What is the resolving power of the objective is used in oil with an index of refraction of 1.45?

d. Would using a longer wavelength improve the resolution? Why or why not?

Answer 1

given

objective diameter, d = 1cm

focal length, f = 2.8 mm

lambda = 550 nm

a.

color of 550 nm light = Yellow.

b.

The minimum resolvable distance between between two objects is called resolving power of a microscope .

RP = 0.61*o/ NA

The angle made by the object

= tan^-1(D/2 / F) = tan^-1(0.01/2 / 2.8*10^-3)

= 60.67^o

Numerical aperture of object lens is

NA = n*sin

for air n = 1

NA = 1*sin60.67

NA = 0.87

So,

RP = 0.61*550*10^-9 / 0.87

RP = 385.63 nm

c.

NA = 1.45*sin60.67 = 1.26

RP = 0.61*550*10^-9 / 1.26

RP = 266.26 nm

d.

using a longer wavelength will increase RP, thereby reducing the resolution ( as resolution is how small can the distance between two points can be for them to be visible distinctively)