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Please see the following question → link(http://freepdfhosting.com/0ed4fb0fe1.pdf) I have solved the first part, but instead of a positive sign, I get a negative one. This is due to a printing error in the question. Now in part b of the question, I get the answer by simply differentiating the optical path length with respect to 'closest distance' and I get the required answer, but I don't really understand why. Can you please tell why is the differential of optical path length equal to the angle turned by the light?

Note:- Make suitable approximations wherever necessary.

My solution :- (https://i.imgur.com/28TFOHo.jpg?1)
With the help of a neat labelled diagram, show the image formation by a compound microscope when the final image is formed at the least distance of distinct vision. write the expressions for its magnifying power in terms of parameters related to the microscope.
Derive the mirror formula.what is the corresponding formula for a thin lens
A diverging lens, with a focal length of -7 cm is placed 46 cm behind the converging lens. Relative to the diverging lens, where is the image (of the candle) formed by the converging lens?
how we define object pin and image pin while performing an experiment to find out the focal lenght of lenses???
The velocity of light in the core of a step index fiber is 2.01x108 m/sec, and
the critical angle at the core-in cladding interfaces 80 degree .Determine the
numerical aperture and the acceptance angle at the fiber in air, assuming it
has a core diameter suitable for consideration by ray analysis .The velocity of
light in vacuum is 3x 108 m/sec
A GeO2-doped silica-based optical fiber has the following parameters: (i) step-index
profile, (ii) refractive index difference at the core of 0.5%, and (iii) core diameter of
9.0 μm
(a) Calculate the refractive index of the fiber core and cladding at 1.310 and 1.55 μm
(b) What is the estimated loss of this fiber at the wavelengths mentioned?
(c) What are the V parameters of the fiber at these wavelengths?
You ordered a converging lens of focal length 3 m but the company delivered a lens whose focal length was only 1 m. You do not have time to wait for a replacement so you decide to correct the problem by placing a diverging lens next to the lens they sent you. What must the focal length be for this diverging lens?
A converging lens of focal length 24 cm is placed next to a converging lens of length 50 cm. What is the effective focal length for this combination?
A darkened room has a tiny aperture in the roof through which sunlight enters when the sun is directly overhead. What is the size of the sun's image on the floor 12 ft below the aperture? the sun is 93 million miles away, and its diameter is 865,000 miles.