1.

In the given figure, the faces of prism ABCD made of glass with a refractive index n form dihedral angles /_A=90^(@),/_B75^(@),,/_C=135^(@) & /_D=60^(@) (The Abbe's prism) .A beam of light falls on face AB & after total internal reflection from face BC escapes through face AD.Find the range of n and angle of incidence alpha of the beam onto face AB, if a beam that has passed through the prism in this mahner is perpedicular to the incident beam.

Answer»


Solution :For the figure since incidence angle at FACE `AB` is `alpha` and REFRACTION angle is `r` , condition that emergent rayis perpndicular to incidence RAY `rArr` angle of EMERGENCE at face `QD` is `alpha`
`rArr` incidence angle at face `QD` is `r.`
In quadrlateral `PQDC 15^(@)+r+135^(@)+r+90=180^(@)`
Now, `75^(@)-r=45^(@)gtcrArr(1)/(sqrt2)gt(10/(N)rArrngtsqrt2`
Also, `sin alpha =n sin r =n sin 30^(@)=(n)/(2)`
`rArr n=2sin alpha rArr (n)/(2)le1rArrnle2`
`therefore sqrt2lenle2` and `(sin alpha)/(sin r)=n rArrsqrt2 le'2sin alphale2`
`rArr (1)sqrt2)ltsin alpha le1 rArr45^(@)ltalphale90^(@)`.


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