# Homework Help: Ratio of a ray of light with a refracted ray

1. Jan 20, 2007

### anantchowdhary

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)

2. Jan 20, 2007

### Staff: Mentor

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

3. Jan 20, 2007

### anantchowdhary

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

4. Jan 20, 2007

5. May 7, 2007

### krateesh

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....

6. May 7, 2007

### anantchowdhary

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

7. May 7, 2007

### krateesh

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

8. May 8, 2007

### anantchowdhary

Well no...this was in two different cases

9. May 8, 2007

### Weimin

Length of a ray? How do you define that?

10. May 8, 2007

### anantchowdhary

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

11. May 8, 2007

### Weimin

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!

Last edited: May 9, 2007