Q37 of 37 Page 1

Derive mirror equation for a convex mirror. Using it, show that a convex mirror always produces a virtual image, independent of the location of object.

OR


(a) Draw a ray diagram for final image formed at distance of distinct vision (D) by a compound microscope and write expression for its magnifying power.


b) An angular magnification (magnifying power) of 30x is desired for a compound microscope using as objective of focal length 1.25cm and eye piece of focal length 5cm. How will you set up the compound microscope?


Let us consider the convex mirror of focal length = f

The object is placed on principle axis.


Distance between object and the mirror= u


The distance between the image and the mirror = v



Using the ray diagram








Similarly,



But DE=AB and when the aperture of the mirror is very small then EF= PF


Hence, equation (ii) becomes





By looking at the diagram, PF= f; PB1=v; PB = u, PC= 2f, therefore,







Dividing the above equation (4) by uvf, we get




For a convex mirror: focal length f is always positive


∴ f >0


Since the object is on the left of the convex mirror, u<0



Using the above formula, we can conclude that v is positive if the image is at the back of the mirror. Therefore, the image is virtual whatever be the value of u.


OR


The magnification of the microscope is given by m= mome where, mo is the magnification due to objective lens and me is the magnification due to eyepiece of microscope.


Magnification of objective lens



Magnification of eyepiece




b) Given: angular magnification = 30


Focal length of eyepiece fe = 5cm


Focal length of objective fo = 1.25 cm


The image formed at least distance of vision= d= 25cm


Magnification of eyepiece me=



Magnification of objective mo = m/ me





Now using, lens makers formula,





Again, using lens maker’s formula for eyepiece,






The distance between object and eyepiece = 4.17 cm


Separation between the objective and eyepiece= 4.17+7.5 = 11.67 cm


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(a) Using Gauss’s law, derive expression for intensity of electric field at any point near the infinitely long straight uniformly charged wire.

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OR


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OR


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