Question

speed of light is 3×10^8 meter/sec in vacuum . what will be it's in diamond of refractive index. 2•5
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Answer 1

Given :-

• Speed of light in vacuum (c) = 3 × 10⁸ m/s
• Refractive index of diamond (n) = 2.5

To Find :-

• Speed of light in diamond (v) = ?

Solution :-

$\red\bigstar \;\sf{Refractive \; Index\; (n) = \frac{\textsf{Speed of light in vacuum (c)}}{\textsf{Speed of light in medium (v)}}}$

⌬ Putting the values in the formula

$\blue\bigstar\;\sf{n = \dfrac{c}{v}}$

$\sf{\implies 2.5 = \dfrac{3 \times 10^8 \; m/s}{v}}$

$\sf{\implies v = \dfrac{3 \times 10^8 \; m/s}{2.5}}$

$\sf{\implies v = \dfrac{3 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10\times 10\times 10\times 10}{25}}$

$\sf{\implies v= 120000000 \; m/s}$

$\sf{\implies v = 12 \times 10^7 \; m/s}$

∴ The speed of light in diamond is 12 × 10⁷ m/s.