Question

thickness of the glass of spectacle is 2 mm and refractive index of its glass is 1.5. calculate time take by light to cross this thickness​

Answer 1

Given:

✰ Thickness of the glass = 2 mm

✰ Refractive index of its glass = 1.5

To calculate:

✠ Time take by light to cross this thickness.

Solution:

Light has a constant speed of 3 × 10⁸ ms⁻ for all colours or wavelength in vacuum.

⤳ Speed of light in glass, v = c/μ

[ N.B: μ is the symbol for refractive index. Here, we will substitute the value of refractive index of glass in μ. ]

⤳ Velocity of light in glass = (3 × 10⁸)/1.5

⤳ Velocity of light in glass = (3 × 10⁸ × 10)/15

⤳ Velocity of light in glass = (30 × 10⁸)/15

⤳ Velocity of light in glass = (10 × 10⁸)/5

⤳ Velocity of light in glass = 2 × 10⁸ m/s or ms⁻

Nature of the units should be same, else calculations will be wrong.

➛ 1 mm = 1 × 10⁻³ m

➛ 2 mm = 2 × 10⁻³ m

∴ The thickness of the glass = 2 × 10⁻³ m

Now,

➤ Time take by light to cross this thickness = Thickness of glass/Velocity of light in glass

➤ Time take by light to cross this thickness = ( 2 × 10⁻³ m )/( 2 × 10⁸ m/s )

➤ Time take by light to cross this thickness = 10⁻³/10⁸ s

➤ Time take by light to cross this thickness = 10⁻³⁻⁸ s

➤ Time take by light to cross this thickness = 10⁻¹¹ s

∴ Time take by light to cross this thickness of the glass = 10⁻¹¹ s

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