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_{PH203KUZMASPRING2014}
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: