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Please explain what is Fresnel equation with a sample problem

Asked by sureshkalanjoor 23rd October 2016, 12:57 PM
Answered by Expert
Answer:
begin mathsize 12px style From space the space theory space of space diffraction space of space light space at space straight a space single space slit comma space the space angle space of space difrraction space for space central space maximum space is space given space as
straight theta space almost equal to space sin space straight theta space equals space straight lambda over straight a
In space travelling space straight a space distance space straight Z comma space due space to space diffraction space of space light comma space the space half space angular space width space of space the space beam space would space become space open parentheses Zλ over straight a close parentheses
This space beam space width space will space become space more space than space width space of space the space slit space left parenthesis straight a right parenthesis.
rightwards arrow space open parentheses Zλ over straight a close parentheses space greater or equal than space straight a
The space above space is space possible space only space when space straight Z space greater or equal than space straight a squared over straight lambda
Here comma space straight a squared over straight lambda equals straight Z subscript straight F space is space the space Fresnel space distance.
The space Fresnel space distance space is space the space minimum space distance space straight a space beam space of space light space can space travel space before space its space deviation space from space straight space line space path space due space to space diffraction space becomes space significant space or space noticeable.
Example colon space Average space wavelenght space of space visible space light comma space straight lambda space equals space 6000 space stack straight A space with straight o on top equals space 6 space cross times space 10 to the power of negative 7 end exponent space straight m
Diameter space of space pupil space of space human space eye comma space straight a space equals space 1 space mm space equals space 10 to the power of negative 3 end exponent space straight m
therefore straight Z subscript straight F equals straight a squared over straight lambda equals fraction numerator open parentheses 10 to the power of negative 3 end exponent close parentheses squared over denominator 6 space cross times space 10 to the power of negative 7 end exponent end fraction equals 10 over 6 equals 1.67 space straight m
This space means space width space of space the space beam space due space to space diffraction space does space not space become space more space than space 1 space mm comma space unless space distance space travelled space by space the space beam space is space more space than space 1.67 space straight m. end style
Answered by Expert 24th October 2016, 12:37 PM
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