# Ratio of a ray of light with a refracted ray

Hey sum1 please tell me that :

if d1=Ray of light through a glass slab(dotted line ie extension of unrefracted ray)

and if d2=Refracted ray

is d1/d2=mu(refractive index)

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jtbell
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How do you divide two light rays? What kind of quantity are $d_1$ and $d_2$? Angle, distance, wavelength, whatever?

d1 is the length of the unrefracted ray(extension of the incident ray into the glass slab) .d2 is the length of refracted ray

Friend ! u r saying that what's the ratio of lengths of rays - the extended incident one and the refracted one......in normal diagram u join the initial rays such that triangle formed by normal & inc. ext. =~ triangle by normal & incident(initial) ray.....now....apply geo. u get d1/d2 =sin(90-r) / sin(90-i) which is not equal to mu...as angles formed are i & r & not their complements....

ofcourse i kno that.....but thats wat happens when u do it experimentally

I am sure the angles u took in experiments was pi/4..45....and students often take it....

Well no...this was in two different cases

Length of a ray? How do you define that?

Well.....if u sketch the path of light...and then measure the length it covered
before exiting the slab

So they are not true.

Call h be the thickness of the slab, then

d1=h/cosi
d2=h/cosr

where i and r are initial and refraction angles

It's clear that d1/d2=cosr/cosi, while n=sini/sinr

They are equal only if sinrcosr=sinicosi or i+r=90 degrees

or tani=n

Just true at Brewster angle!

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