Light travels with a speed of ` 2xx 10^(8)ms^(-1)` in crown glass of refractive index 1.5. What is the speed of light in dense flint glass of refractive index 1.8 ?

Options

A. `1.33 xx 10^(8) ms^(-1)`
B. `1.67 xx 10^(8) ms^(-1)`
C. `2.0 xx 10^(8) ms^(-1)`
D. `3.0 xx 10^(8) ms^(-1)`

Explanation

To find the speed of light in dense flint glass with a refractive index of 1.8, we can use the relationship between the speed of light in a medium and its refractive index. The refractive index (μ) is defined as:

\[ \mu = \frac{c}{v} \]

Where:
- \( \mu \) = refractive index of the medium
- \( c \) = speed of light in vacuum (approximately \( 3 \times 10^8 \, \text{m/s} \))
- \( v \) = speed of light in the medium

### Step 1: Calculate the speed of light in vacuum (c)
Since we know that the speed of light in crown glass is given as \( 2 \times 10^8 \, \text{m/s} \) and its refractive index is \( 1.5 \), we can first find the speed of light in vacuum using the refractive index formula.

\[ \mu_{cg} = \frac{c}{v_{cg}} \]

Substituting the known values:

\[ 1.5 = \frac{c}{2 \times 10^8} \]

### Step 2: Solve for c
Rearranging the equation to solve for \( c \):

\[ c = 1.5 \times (2 \times 10^8) \]

Calculating this gives:

\[ c = 3 \times 10^8 \, \text{m/s} \]

### Step 3: Find the speed of light in dense flint glass (v_fg)
Now, we can use the refractive index of dense flint glass, which is \( 1.8 \), to find the speed of light in that medium.

Using the refractive index formula again:

\[ \mu_{fg} = \frac{c}{v_{fg}} \]

Substituting the known values:

\[ 1.8 = \frac{3 \times 10^8}{v_{fg}} \]

### Step 4: Solve for v_fg
Rearranging the equation to solve for \( v_{fg} \):

\[ v_{fg} = \frac{3 \times 10^8}{1.8} \]

Calculating this gives:

\[ v_{fg} = \frac{3 \times 10^8}{1.8} = 1.67 \times 10^8 \, \text{m/s} \]

### Final Answer
The speed of light in dense flint glass is approximately:

\[ v_{fg} = 1.67 \times 10^8 \, \text{m/s} \]

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