The refractive index of denser medium with respect to rarer medium is 1.125. The difference between the velocities of light in the two media is 0.25 ×10^8 m/s. Find the velocities of light in the two media and their refractive indices.
Answers
Explanation:
A
2.0×10
8
m/s; 2.25×10
8
m/s
Velocity of light in denser medium V
r
=
μ
2
ν
V
r
=
μ
2
3×10
8
Velocity of light in rarer medium V
d
=
μ
1
ν
V
d
=
μ
1
3×10
8
Given,
μ
1
μ
2
=1.125
μ
2
=1.125 μ
1
Given, V
r
−V
d
=0.25×10
8
⟹
μ
1
3×10
8
−
μ
2
3×10
8
=0.25×10
8
So, V
d
=2×10
8
m/s and V
r
=2.25×10
8
m/s
Explanation:
n ( denser)/ n(rarer) = V(r)/V(d)
1.125 = V(r) / V(d). _______1
V(r) - V(d) = 0.25 x 10⁸ ______2
V(d) x 1.125 - V(d) = 0.25 x 10⁸
V(d). = 0.25 x 10⁸/ 0.125
= (25 x 10⁶ x 10³ )/ 125
= 10⁹/5
= 2 x 10⁸ m/s
V(r) = 2 x 10⁸ x 1.125
= 2.250 x 10⁸ m/s
refractive index of denser =n(d) / n(air) =2 x 10⁸/ 2 x 10⁸
= 1
refractive index of rarer = n(r)/n(air) = 2 x 10⁸/ 2.250 x 10⁸
= 2000/ 2250 = 200/225 = 40/45 = 8/9.