Answer

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**Hint:**To solve this question, we need to find out the angle made by the incident ray with the normal to the surface of the mirror. Then we have to use the law of reflection which relates the angle of incidence and angle of reflection, to find out the required value of the angle between the normal and the reflected ray.

**Complete step-by-step solution**

Since the type of mirror is not mentioned in the question, so we assume that the mirror in question is a plane mirror. According to the question, the ray is incident at an angle of $ {38^ \circ } $ with the mirror. By the laws of reflection, we know that the angle of incidence is equal to the angle of reflection. But both the angle of incidence and the angle of reflection are measured with the normal to the mirror at the point of incidence. So first we have to find out the angle made by the incident ray.

Since the incident ray makes an angle of $ {38^ \circ } $ , so the angle made with the normal is given by

$ i = {90^ \circ } - {38^ \circ } $

$ \Rightarrow i = {52^ \circ } $

Now since the angle of reflection is equal to the angle of incidence, the angle of reflection is also equal to $ {52^ \circ } $ .

Thus, the angle between the normal and the reflected ray is equal to $ {52^ \circ } $ .

**Hence, the correct answer is option B.**

**Note**

The value of the angle given in the question is that of the angle made by the incident ray with the mirror. Do not misunderstand it to be the angle made by the incident ray with the normal. Also, the choice of the type of mirror is immaterial. This is because the angle of the ray with the mirror is defined as the angle between the incident ray and the tangent to the mirror at the point of incidence.

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