As we know that,
Observer is standing on the southern hemisphere, facing towards the north and cathode ray is moving away from him, and we know that cathode ray is negatively charged beam, due to the influence of the earth's magnetic field the ray of the cathode beam will start to get deflect.
Applying the right hand thumb rule, then angle between the cathode ray and the magnetic field is parallel to each other, as per the right hand thumb rule,
"F=qvB\\sin \\theta\\hat{n}"
Hence, ray of the light will not get deflect, because here angle is zero.
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