To observe a maximum number of orders in a diffraction grating, which angle should be substituted in the interference pattern formula?

In a diffraction grating, the condition for observing maxima is given by the grating equation:

[ d \sin(\theta) = m \lambda ]

where ( d ) is the distance between grating lines, ( \theta ) is the angle of diffraction, ( m ) is the order of the maximum, and ( \lambda ) is the wavelength of the light used.

To maximize the number of observable orders (maxima), we need to look at the sine function within the range defined by the equation. The sine function reaches its maximum value of 1 at an angle of 90 degrees. By substituting ( \theta = 90^\circ ) into the equation, you can observe that:

[ d \sin(90^\circ) = d \times 1 = d ]

This means that at this angle, the equation allows for the highest order ( m ) that can be satisfied under the constraint of the grating spacing ( d ) and the wavelength ( \lambda ). Beyond this angle, the sine function would exceed unity, making it impossible to have real solutions for maxima.

Angles below 90 degrees will produce smaller sine values, consequently limiting the number of observable orders.