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Answer the following questions: (e) Ra...

Answer the following questions:
(e) Ray optics is based on the assumption that light travels in a straight line. Diffraction effects (observed when light propagates through small apertures/slits or around small obstacles) disprove this assumption. Yet the ray optics assumption is so commonly used in understanding location and several other properties of images in optical instruments. What is the justification?

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Justification based on what is explained in (d). Typical sizes of apertures involved in ordinary optical instruments are much larger than the wavelength of light.
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The lens governing the behavior of the rays namely rectilinear propagation laws of reflection and refraction can be summarised in one fundamental law known as Fermat's principle. According to this principle a ray of light travels from one point to another such that the time taken is at a stationary value (maximum or minimum). if c is the velocity of light in a vacuum the velocity in a medium of refractive index mu is (c)/(mu) hence time taken to travel a distance l is (mul)/(c) if the light passes through a number of media, the total time taken is ((1)/(c))summul or (1)/(c)intmudl if refractive index varies continuously. Now summul is the total path, so that fermat's principle states that the path of a ray is such that the optical path in at a stationary value. this principle is obviously in agreement with the fact that the ray are straight lines i a homogenous isotropic medium. it is found that it also agrees with the classical laws of reflection and refraction. Q. The optical length followed by ray from point A to B given that laws of reflection are obeyed as shown in figure is

The lens governing the behavior of the rays namely rectilinear propagation laws of reflection and refraction can be summarised in one fundamental law known as Fermat's principle. According to this principle a ray of light travels from one point to another such that the time taken is at a stationary value (maximum or minimum). if c is the velocity of light in a vacuum the velocity in a medium of refractive index mu is (c)/(mu) hence time taken to travel a distance l is (mul)/(c) if the light passes through a number of media, the total time taken is ((1)/(c))summul or (1)/(c)intmudl if refractive index varies continuously. Now summul is the total path, so that fermat's principle states that the path of a ray is such that the optical path in at a stationary value. this principle is obviously in agreement with the fact that the ray are straight lines i a homogenous isotropic medium. it is found that it also agrees with the classical laws of reflection and refraction. Q. The optical path length followed by ray from point A to B given that laws of refraction are obeyed as shown in figure.

The lens governing the behavior of the rays namely rectilinear propagation laws of reflection and refraction can be summarised in one fundamental law known as Fermat's principle. According to this principle a ray of light travels from one point to another such that the time taken is at a stationary value (maximum or minimum). if c is the velocity of light in a vacuum the velocity in a medium of refractive index mu is (c)/(mu) hence time taken to travel a distance l is (mul)/(c) if the light passes through a number of media, the total time taken is ((1)/(c))summul or (1)/(c)intmudl if refractive index varies continuously. Now summul is the total path, so that fermat's principle states that the path of a ray is such that the optical path in at a stationary value. this principle is obviously in agreement with the fact that the ray are straight lines i a homogenous isotropic medium. it is found that it also agrees with the classical laws of reflection and refraction. Q. If refractive index of a slab varies as mu=1+x^(2) where x is measured from one end then optical path length of a slab of thickness 1 m is

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