69. a grating with lines uniformly spaced at 775 nm is illuminated by a sodium discharge lamp.

for what range of wavelength will there only be three principal lines generated?

Only  two diffraction orders +1 and -1 are possible

Explanation:

The diffraction net is a system with many uniformly spaced lines, which is described by the expression

      d sin θ = m λ               m = 1, 2, 3,…

Where d is the spread between the lines, λ the wavelength and m is an integer that corresponds to the order of diffraction, all wavelengths

For this case the spacing is

          d = 775 nm

The sodium emission lines are 589.00 nm and 589.59 nm

With this data we can calculate how many diffraction orders are visible

         θ = sin⁻¹ (m λ / d)

m = 1

         λ1 = 589.00 nm

         θ1 = sin⁻¹ (1  589/775)

         θ1 = 49.46 °

         λ2 = 589.59 nm

        θ2 = sin⁻¹ ((1  589.59 / 775)

        θ2 = 49.53 °

m = 2

        λ1 = 589.00 nm

       θ1 = sin⁻¹ (2  589/775)

       θ1 = sin⁻¹ (1.5)

This order is not possible because the sin cannot be greater than 1

m = -1

       λ1 = 589 nm

       θ1 = sin⁻¹ (-1 589/775)

       θ1 = -49.46

       θ= sin⁻¹ ( -1 589.59/775)        

       λ2 = 589.59 nm

       θ2 = -49.53 °

m = -2

       λ1 = 589 nm

       θ1 = sin-1 (-2 589/775)

This order does not occur because the breast cannot be greater than 1

Only  two diffraction orders +1 and -1 are possible

answer: the exterior temperature of commercial jet planes as they leave the stratosphere and return to the ground increases steadily.

explanation:

the lower most layer of atmosphere is troposphere which extends from 0 to 12 km above the surface of the earth. the temperature initially decreases as distance is increased from the earth's surface. commercial jets fly in lower part of the stratosphere. the stratosphere extends upto 50 km. the temperature in stratosphere starts rising again due to presence of ozone which traps the uv rays.

thus, when the planes leave the stratosphere and return to the ground, the exterior temperature increases steadily.