A wedge-shaped thin glass plate of refractive index 1.52 is used to observe fringes of equal thickness. The fringe spacing is 1 mm and the wavelength of light used is 5893 Å. Calculate the angle of the wedge.
1 Answer
To calculate the angle of the wedge, we can use the formula for fringe spacing in a thin wedge-shaped air film. The formula for the fringe spacing \( \Delta x \) is given by:
\[
\Delta x = \frac{\lambda}{2 \mu \cdot \theta}
\]
Where:
Now, let’s plug in the given values and solve for \( \theta \):
\[
\theta = \frac{\lambda}{2 \mu \cdot \Delta x}
\]
Substitute the known values:
\[
\theta = \frac{5893 \times 10^{-10}}{2 \times 1.52 \times 1 \times 10^{-3}}
\]
Let’s calculate it.
The angle of the wedge is approximately \( 0.0111^\circ \).
\[
\Delta x = \frac{\lambda}{2 \mu \cdot \theta}
\]
Where:
- \( \Delta x \) is the fringe spacing (1 mm = \( 1 \times 10^{-3} \) m)
- \( \lambda \) is the wavelength of light (5893 Å = \( 5893 \times 10^{-10} \) m)
- \( \mu \) is the refractive index of the glass (1.52)
- \( \theta \) is the angle of the wedge (in radians)
Now, let’s plug in the given values and solve for \( \theta \):
\[
\theta = \frac{\lambda}{2 \mu \cdot \Delta x}
\]
Substitute the known values:
\[
\theta = \frac{5893 \times 10^{-10}}{2 \times 1.52 \times 1 \times 10^{-3}}
\]
Let’s calculate it.
The angle of the wedge is approximately \( 0.0111^\circ \).