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_{PH203KUZMASPRING2015}
Chapter 27  

Any lens or mirror  Size of Aperture $f$number (dimentionless)  $f$number$=\frac{\text {Focal length}}{\text {diameter of aperture}}=\frac{f}{D}$ 
Any lens or mirror  Refractive power Ability to refract light SI Unit: ${\text m}^{1}=\,$dpt  Refractive power = $\frac{1}{f}$ 
Magnifying glass  Angular magnification of the magnifying glass  $M=$ $\frac{\theta_\text{with}}{\theta_\text{without}}$ $\approx\frac{\;\frac{h_o}{f}\;}{\frac{h_o}{N}}=\frac {N}{f}$ 
Angle without a magnifier N = near point of a person  $\theta_\text{without}=\frac{h_o}{N}$  
angle with magnifier  $\theta_\text{with}$ $=\frac{h_o}{d_o}$ $\approx\frac{h_o}{f}$  
image at infinity  $M=$ $\frac{N}{f};\;\;\;\;$ $m=\infty$  
image at a person's near point  $M=m=$ $1 + \frac{N}{f}$  
Simple compound microscope  The magnification produced by the objective $d_o \approx f_\text {objective}$  $m_\text {objective}=\frac{d_i}{d_o}$ $\approx \frac{d_i}{f_\text {objective}}$ 
Angular magnification of the eyepiece  $M_\text {eyepiece}=\frac{N}{f_\text {eyepiece}}$  
Total angular magnification of the microscope: ($$) sign means an inverted image  $M_\text{total}=m_\text{objective}\!\cdot\! M_\text{eyepiece}$ $=\left(\frac{d_i}{f_\text{objective}}\right)\left(\frac{N}{f_\text{eyepiece}}\right)$ 

Length of microscope  $L\approx\,d_i+\,f_\text{eyepiece}$  
Simple compound telescope  Total angular magnification of the telescope  $M_\text{total}=\frac{\theta'}{\theta}$ $=\frac{f_\text{objective}}{f_\text{eyepiece}}$ 
Object's angular size  $\theta=\frac{h_i}{f_\text{objective}}$  
Final image angular size  $\theta'=\frac{h_i}{f_\text{eyepiece}}$  
Length of telescope (focus on $\infty$)  $L=f_\text{objective}+\,f_\text{eyepiece}$ 
Assuming the depth of the eye is 2.5 cm, find the focal distance for your eye's lens necessary to focus either at the far point ($\infty$) or at the near point N = 17 cm.
Steps:
A farsighted person's near point (the closest point of sharp focus) is at $N>20$ cm. Calculate, approximately (using refractive power approximation) and precisely, what corrective lens should be placed 2 cm in front of the person's eye to enable sharp focus at 20 cm. Consider the following cases of farsightedness: $N=2\,$m, $1\,$m, $60\,$cm, $40\,$cm, $30\,$cm, $25\,$cm.
Steps:
A nearsighted person's far point (the farthest point of sharp focus) is at $X$. Calculate, approximately (using refractive power approximation) and precisely, what corrective lens should be placed 2 cm in front of the person's eye to enable sharp focus far away (at $\infty$). Consider the following cases of nearsightedness: $X=4\,$m, $2\,$m, $1\,$m, $50\,$cm, $30\,$cm, $20\,$cm.
Steps:
A simple, 35mm film camera is used in landscape mode to take a picture of a 1.7m tall person from a distance $d_o=5\,$m. Assuming the camera's only thin lens is $d_i=8\,$cm from the film, find the focal distance of the lens required for this image. Also, find the image size and orientation. Will it fit on the 35 mm film?
Steps:
A microscope that consists of the objective with the focal distance $f_\text{objective}=4\,$mm and an eyepiece $\big(\,f_\text{eyepiece}=2\,{\text{cm}}\big)$, is used by a person with a near point $N=20\,$cm at the following (angular) magnifications:
Find, using an approximate formula for microscope magnification, as well as using a precise calculation, the distance $L$ between the two pieces of optics necessary for each of the above magnifications, assuming the most comfortable viewing distance of the final image $d_i^\text{eyepiece}=\infty$.
Steps:
A simple telescope of length $L=40\,$cm has two options for the eyepiece lens:
Calculate the focal distance of the objective lens necessary for each option, as well as the (magnitude of the total angular) magnification in each case.
Steps:
$\;\;$ Using the $L=$ $f_\text{objective}+f_\text{eyepiece}$ formula,
Binoculars using a simple telescope design have $\;f_\text{objective}\!=\!20\,$cm and $\;f_\text{eyepiece}\!=\!0.5\,$cm. The distance $L$ between the two lenses can be adjusted to focus on a specific object at a distance $d_o$. Find the value of $L$ necessary to focus on
Also find the magnitude of angular magnification in each case.
Steps:
What if the f number in dim light when the pupil has expanded to 6.0 mm?
I also got the wrong answer for calculating the f number when the diameter is 2.0 mm in bright light.
Part a. In the HW solutions it has a negative sign in the equation $M=\frac{f_\text{objective}}{f_\text{eyepiece}}$. Is this because the eye piece is concave? I am just confused why it says to set the magnification equal to the negative of the ratio of the focal lengths.
Very good question! Traditionally, telescope magnification is quoted without any regard to the + or $$ signs, since very few astronomers care if a given star looks upsidedown or not. But technically speaking, the simplest telescope design discussed in class always inverts the image (makes it upsidedown), so, according to the definition of the magnification, it should be negative. — Prof. Nicholas Kuzma 2015/05/12 23:51
A person's prescription for her new bifocal glasses calls for a refractive power of 0.400 diopters in the distancevision part, and a power of 1.85 diopters in the closevision part.
I did $1/0.04$ and got $250$ cm, so 2.52 m for the far point. I then did $1/561/25$ and got $0.45$ m for the near point. I even had my tutor help me, and we could not get the correct answer.
— Prof. Nicholas Kuzma 2015/05/13 00:21
The mediumpower objective lens in a laboratory microscope has a focal length $f_\text{objective} = 4.00$ mm. If this lens produces a lateral magnification of $40.0$, what is its “working distance”; that is, what is the distance from the objective to the objective lens?