A glass slab of diameter D=20cm is made at the base of a ship as shown in figure. Diameter of glass slab is much larger than the thickness of the glass slab. The area 'S' of the field of view at the sea bottom if `mu_("water")=4//3`, `mu_("glass")=3//2` & the depth of sea base beow the slab is `h=sqrt(7)m` is

Options

A. `9pim^(2)`
B. `((80)/(5))m^(2)`
C. `(1408)/(17)m^(2)`
D. `(pi)/(100)m^(2)`

Answer

A

Explanation

`sinalpha=(1)/(mug)`
`mu_(w)sinbeta=mu_(g)sinalpha`

or `mu_(w)sinbeta=mu_(g)xx(1)/(mu_(g))=1`
`beta=sin^(-1)((1)/(mu_(w)))`
`thereforeA_("base")=piR^(2)=pih^(2)tan^(2)beta=(pih^(2))/((mu_(w)^(2)-1))[becausetanbeta=(1)/(sqrt(mu_(w)^(2)-1))]`