Practicing Success

Target Exam

CUET

Subject

Physics

Chapter

Ray Optics

Question:

Inside a substance such as glass or water, light travels more slowly than it does in a vacuum. If c denotes the speed of light in a vacuum and v denotes its speed through some other substance, then $v=\frac{c}{n}$

Where n is a constant called the index of refraction.

To almost exact approximation, a substance’s index of refraction does not depend the wavelength of light. For instance, when red and blue light waves enter water, they both slow down by about the same amount. More precise measurements, however, reveal that n varies with wavelength. Table 1 presents some indices of refraction of Cutson glass, for different wavelengths of visible light. A nanometer (nm) is $10^{–9}$ meters. In a vacuum, light travesl at $c = 3.0 × 10^8 m/s$. Indices of refraction of Cutson glass (Table 1)

approximate

wavelength in vacuum (nm)  

n

yellow

580

1.500

yellow orange  

600

1.498

orange

620

1.496

orange red

640

1.494

For blue green of wavelength 520 nm, the index of refraction of Cutson glass is probably closest to:

Options:

1.49

1.50

1.51

1.52

Correct Answer:

1.51

Explanation:

Table suggests a linear relationship between wavelength and index of refraction. Starting with yellow light, we can extrapolate with linear relationship to blue green light.

As compared to yellow light waves, blue green light waves are 60 nm shorter (520 nm vs. 580 nm). By reading table from bottom to top, we see that each 20 nm decreases in wavelength corresponds to a 0.002 increase in n. So, since yellow and blue green differ in wavelength by 60 nm, the corresponding n’s should differ by 0.006.

$n_{blue\, green} = n_{yellow} + 0.006 = 1.500 + 0.006 = 1.506$ which is closer to 1.51 than it is to 1.50.

You can also address this question by extrapolating table.

blue green

520

1.506

 

540

1.504

 

560

1.502

yellow

580

1.500

yellow orange

600

1.498

orange

 620 

 1.496 

orange red

640

1.494