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1997

(c) A portion of a straight glass rod of diameter d and refractive index n is bent into

an arc of a circle of mean radius R, and a parallel beam of light is shone down

it, as shown in Figure 15C. (i) Derive an expression in terms of R and d for the no-

angle of incidence i of the central ray C on reaching the glass-to-air surface at

the circular arc. (ii) Show that the smallest value of R which will allow all the

Flight to pass around the arc is given by

TIR=

Sin 92

opposite

of Incidule

hoe merim

When !!

add(n + 1)

R

R-D

2(n-1)

Wind/nLight

d

Figure 15C

R

inci

Fig: 1

Fig: 2