- #1
StillAnotherDave
- 75
- 8
- Homework Statement
- Change in resolution to microscope.
- Relevant Equations
- ##NA=nsin\theta =\frac{nD}{2f}##
##x_{min}=1.22\frac{f\lambda }{D}##
Hello folks,
I have the two following questions I'm working on:
Q1
An optical microscope uses a lens with NA = 0.7 and a focal length of f = 20 mm. What is the smallest spatial distance that can be resolved if a wavelength of λ = 633nm is used? An iris is introduced in front of the lens with a diameter of 10 mm at a distance of 10 mm from the object. How does the resolution of the microscope change?
Q2
A digital camera equipped with a f = 300mm focal length lens is mounted on a survey satellite orbiting the Earth at a height of 150 km. The camera must be designed such, that photographs with 1.2m in spatial resolution can be taken. Determine the diameter of the lens. The lens casts an image onto the digital camera with a finite pixel size. Calculate the pixel size required to allow this spatial resolution. The wavelength of light can be assumed to be λ = 500 nm.The second parts of each question (in bold) are what I'm struggling with. I've worked out the smallest spatial distance in Q1 and the diameter in Q2. Any help on how to tackle (1) the introduction of the iris into Q1, and the pixel size in Q2.
For Q1:
$$NA=\frac{nD}{2f}$$
therefore, ##D=28mm## (assuming ##n=1## as given in a previous part of the question). Plugging this value into:
##x_{min}=1.22\frac{f\lambda }{D}## gives ##x_{min}=552nm##
For Q2:
$$NA=\frac{nD}{2f}$$
Plugging in the given values for ##NA##, ##f## and ##\lambda## gives ##D=153nm##
I have the two following questions I'm working on:
Q1
An optical microscope uses a lens with NA = 0.7 and a focal length of f = 20 mm. What is the smallest spatial distance that can be resolved if a wavelength of λ = 633nm is used? An iris is introduced in front of the lens with a diameter of 10 mm at a distance of 10 mm from the object. How does the resolution of the microscope change?
Q2
A digital camera equipped with a f = 300mm focal length lens is mounted on a survey satellite orbiting the Earth at a height of 150 km. The camera must be designed such, that photographs with 1.2m in spatial resolution can be taken. Determine the diameter of the lens. The lens casts an image onto the digital camera with a finite pixel size. Calculate the pixel size required to allow this spatial resolution. The wavelength of light can be assumed to be λ = 500 nm.The second parts of each question (in bold) are what I'm struggling with. I've worked out the smallest spatial distance in Q1 and the diameter in Q2. Any help on how to tackle (1) the introduction of the iris into Q1, and the pixel size in Q2.
For Q1:
$$NA=\frac{nD}{2f}$$
therefore, ##D=28mm## (assuming ##n=1## as given in a previous part of the question). Plugging this value into:
##x_{min}=1.22\frac{f\lambda }{D}## gives ##x_{min}=552nm##
For Q2:
$$NA=\frac{nD}{2f}$$
Plugging in the given values for ##NA##, ##f## and ##\lambda## gives ##D=153nm##