When the light from a light bulb is reflected by a diffraction grating, a continuous band spectrum is obtained (like a rainbow). When the light from a metal salt in a flame is reflected from a diffraction grating, visible, discrete lines are observed. What causes this line spectra?

The light of a light bulb contains all the wavelengths of visible band which on passing through diffraction grating appear in the form of continuous spectra.

Discrete lines are observed when the electron makes a transition from higher orbit to lower orbit releasing a photon having energy which is equivalent to the energy difference between the two orbits.

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find the sum of the two horizontal vectors and the sum of the two vertical vectors

isoceles right angled triangle