Answer:
(a) 5.45 m
(b) no change
Explanation:
refractive index of water, n = 1.333
h = 2.4 m
Let the radius of circle is r.
Here we use the concept of total internal reflection.
Let i be the angle of incidence.
By using Snell's law
Refractive index of water with respect to air is the ratio of Sin of angle of incidence to the Sin of angle of refraction.
here refraction takes place from denser medium to rarer medium
So, [tex]\frac{1}{n}=\frac{Sin i}{Sin r}[/tex]
Here, angle r is 90 for total internal reflection
[tex]\frac{1}{1.33}=\frac{Sin i}{Sin 90}[/tex]
Sin i = 0.75
i = 48.6°
According to the triangle ΔOAB
[tex]tan i = \frac{AB}{OA}[/tex]
[tex]tan 48.6 = \frac{r}{2.4}[/tex]
r = 2.73 m
Diameter = 2 r = 2 x 2.73 = 5.45 m
Thus, the diameter of the circle is 5.45 m.
(b) As the value of r depends on the angle of incidence i and angle of incidence depends on the value of refractive index. As refractive index is constant, so the value of diameter remains same.
