Question

define critical angle . obtain the formula for critical angle​

Answer 1

angle at which total internal reflection form called as critical angle

formula and condition is

angle A<critical angles÷2

and formula is sin inverse(1÷refrctive index)

Answer 2

the least angle of incidence at which total reflection takes place

Illustration of critical angle

Illustration of critical angle

critical angle: AOB, AO'B', AO''B'' angles of incidence; AOC refracted ray; AO''C'' totally reflected ray; AO'B' critical angle

Derivation :

Critical angle = Θi that gives a Θr value of 90-degrees

According to Snell’s Law equation, a generic equation for finding the critical angle can be derived easily.

ni *• sine(Θi) = nr • sine (Θr)

ni • sine(Θcrit) = nr • sine(90 degrees)

ni • sine(Θcrit) = nr

sine(Θcrit) = nr/ni

Θcrit= sine-1 (nr/ni) = invsine (nr/ni)

Solved Examples

Example 1

Find the critical angle for the crown glass-air boundary.

The solution to the problem requires the use of the above equation for the critical angle.

Θcrit = sin-1 (nr/ni) = invsine (nr/ni)

Θcrit = sin-1 (1.000/1.52) = 41.1 degrees