A ray of light is incident on a glass slab of thickness t, at an angle i,r is the angle of refraction in the glass slab. Distance travelled in the glass slab is

Options

A. `tcosr`
B. `ttanr`
C. `(t)/(cosr)`
D. `(t)/(sinr)`

Explanation

To solve the problem of finding the distance traveled by a ray of light in a glass slab of thickness \( t \), we can use some basic trigonometry. Let's break it down step by step.

### Step 1: Understand the Geometry
When a ray of light enters a glass slab at an angle of incidence \( i \), it refracts and travels through the slab at an angle of refraction \( r \). The thickness of the slab is given as \( t \).

### Step 2: Identify the Points
Let's label the points:
- Point A: The point where the light enters the glass slab.
- Point B: The point where the light exits the glass slab.
- Point O: The point where the light is refracted inside the slab.

### Step 3: Draw a Right Triangle
Inside the glass slab, we can visualize a right triangle formed by:
- The thickness of the slab \( t \) as one side (the vertical side).
- The distance traveled by the light in the glass slab as the hypotenuse.

### Step 4: Use Trigonometry
In the right triangle OAB:
- The angle at point O is \( r \).
- The side opposite to angle \( r \) is the thickness \( t \).
- The hypotenuse is the distance traveled by the light in the slab, which we will denote as \( OA \).

Using the cosine function:
\[ \cos(r) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{BO}{OA} \]
Here, \( BO \) is the thickness \( t \).

### Step 5: Rearranging the Equation
From the above equation, we can rearrange it to find \( OA \):
\[ OA = \frac{t}{\cos(r)} \]

### Step 6: Conclusion
Thus, the distance traveled by the light in the glass slab is given by:
\[ OA = \frac{t}{\cos(r)} \]

### Final Answer
The distance traveled by the light in the glass slab is \( \frac{t}{\cos(r)} \).

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