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A slit or an aperture diffracts light. Even then we say light travels in a straight lineand ray optics is valid. Comment. |
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Answer» Solution :We have studied that a slit of WIDTH a diffracts a beam of light. Half angular width a central maximum is `theta ~~ sin theta = (lambda)/(a)` This is the half angular size of BRIGHT central maximum. In travelling a distance `Z`, the diffracted beam, therefore, acquires a width `Z lambda//a` just due to diffraction. This width will become more than width of slit, i.e. `(Z lambda)/(a)ge a`, when `Z ge (a^(2))/(lambda)` We call `(a^(2))/(lambda) = Z_(F)`, the Fresnel's distance , For example, for human EYE, aperture `a = 3 mm = 3 XX 10^(-3) m and lambda = 5000 Å = 5 xx 10^(-7)m` (for visible light) `Z_(F) = (a^(2))/(lambda) = (3 xx 10^(-3))^(2)/(5 xx 10^(-7)) = 18m` This means width of beam due to diffraction does not become more than `3 mm` unless distance travelled by the beam is more than `18m`. Therefore, we can negelct broadening of beam by diffraction upto distance as large as a few meters. Hence ray optics is valid in all common situations we comeacross. |
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