The refractive index of a medium ' x ' with respect to ' y ' is 2/3 and the refractive index of the medium ' y ' with respect to medium ' z ' is 4/3 . Calculate the refractive index of the medium ' z ' with respect to medium ' x ' .. Find the speed of light in medoum y if speed of light in medium x is 3*10^8 m/s
Answers
Answer:(I) 9/8
(II) 2*10^8m/s
Explanation:
(I) Z/X=?
X/Y=2/3
Y=3X/2...(1)
Y/Z=4/3
Y=4Z/3...(2)
Equate RHS of (1) and (2)
3X/2=4Z/3
9X=8Z
Therefore, Z/X=9/8.
Hence, refrective index of medium Z w.r.t medium X is 9/8.
(II)Let speed of light in medium 'Y' be 'V'
Let speed of light in medium 'X' be 'C' i.e. 3*10^8m/s
So, Y/X=3/2...(3)
C/V=3*10^8/V...(4)
Equate RHS of (3) and (4)
3/2=3*10^8/V
So, 3V=3*10^8*2
Therefore, V=3*10^8*2/3
V=10^8*2
Therefore, V=2*10^8m/s
Hence, speed of light in medium Y is 2*10^8m/s
The refractive index of the medium 'z' with respect to medium 'x' is 9/8
The speed of light in medium y with respect to x is 2 × 10⁸ m/s
Given:
Nxy = 2/3
Nyz = 4/3
Explanation:
Nxy = Nx/Ny
Nyz = Ny/Nz
The refractive index of z with respect to x is given as:
Nzx = Nz/Nx = Ny/Nx × Nz/Ny
Nzx = 1/Nxy × 1/Nyz
On substituting the values, we get,
Nzx = 1/(2/3) × 1/(4/3)
Nzx = 3/2 × 3/4
∴ Nzx = 9/8
The refractive index is given by the formula:
Refractive index = (Velocity of light in vacuum)/(Velocity of light in that medium)
The speed of light in y medium is v
The speed of light in x medium is 3 × 10⁸ m/s
The refractive index of medium y with respect to x is given as:
Nyx = 3/2
Now,
3/2 = (3 × 10⁸)/v
∴ v = 2 × 10⁸ m/s