A light ray is incident on an irregular shaped slab of refractive index `sqrt(2)` at an angle of `45^@`with the normal on the incline face as shown in the figure. The ray finally emerges from the curved surface in the medium of the refractive index `mu = 1.514` and passes through point E. If the radius of curved surface is equal to 0.4 m. find the distance OE correct upto two decimal places.

Explanation

Using snell.s law
`mu_(1) sin 45^@ = mu_(2) sin theta`
`theta=30^@`
i.e. ray moves parallel to axis
`mu_(3)/(OE) - mu_(2)/oo = ((mu_(3)-mu_(2))/R)`
OE = 6.056m = 6.06 m