Question

I, recently, submitted the following question to your forum:

Light of wavelength 450nm is incident at right angles to a grating producing second order images with an angle of 70^o between them. What is the number of lines per cm ruled on the grating? I received worked solution - 1.04 x 10⁶ lines per meter = 10440 lines per cm.

Later, this answer was disputed by a fellow studymate. After further research, I found the suggested answer (posited by the writer of the book from which the question originated. Here is the solution given:

From the central fringe to the second order image, the angle subtended is 70/2 = 35^o. Therefore, sin theta = m.lambda.P  $\therefore$ P = sin35^o /2(450 x 10^-9 = 6.4 x 10⁵ m^-1 = 6.4 x 10³ cm^-1

Which is the correct answer? Explain

Answer 1

The condition for central maxima for diffraction is Here, mis the order of the fringe, d is the separation of the slits. (2) (450x10"m) sin[ 70° 957.759x10"m fn Number of lines is the reeciprocal separation of the slits 957.759x10°m100cm fn 957759×10-7 cm 10 957.759 cm 10,440ines /cm.