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Geometrical Optics question

2022 · 26 Jun · Shift 1 · Q64
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  5. /2022 · 26 Jun · Shift 1 · Q64

Geometrical Optics question

2022 · 26 Jun · Shift 1 · Q64

JEE MainPhysicsGeometrical OpticsNumerical+4 / −1
A light ray is incident, at an incident angle θ\thetaθ 1, on the system of tow plane mirrors M1 and M2 having an inclination angle 75 ∘^\circ∘ between them (as shown in figure). After reflecting from mirror M1 it gets reflected back by the mirror M2 with an angle of reflection 30 ∘^\circ∘. The total deviation of the ray will be ‾\underline{\hspace{2cm}}​ degree. JEE Main 2022 (Online) 26th June Morning Shift Physics - Geometrical Optics Question 117 English
Numerical answer
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Correct answer: 210

  1. Key fact for two successive reflections from inclined plane mirrors
    If a ray reflects successively from two plane mirrors inclined at an angle ϕ\phiϕ, then the net change in direction of the ray depends only on ϕ\phiϕ and is equal to 2ϕ.2\phi.2ϕ. Here, ϕ=75∘.\phi = 75^\circ.ϕ=75∘. So the angle through which the direction of the ray turns is 2×75∘=150∘.2\times 75^\circ = 150^\circ.2×75∘=150∘.

  2. Meaning of total deviation
    In optics, the total deviation is the angle between the original straight-line direction of the incident ray (produced forward) and the final emergent ray.
    Since the ray has turned by 150∘150^\circ150∘, the deviation is the reflex angle associated with this geometry: δ=360∘−150∘=210∘.\delta = 360^\circ - 150^\circ = 210^\circ.δ=360∘−150∘=210∘.

  3. Check with given extra data
    The given reflection at M2M_2M2​ is 30∘30^\circ30∘; this helps fix the actual path but does not change the standard result that two reflections from mirrors inclined at 75∘75^\circ75∘ produce a net turning of 150∘150^\circ150∘, hence total deviation 210∘210^\circ210∘ in the convention used here.

  4. Final answer 210\boxed{210}210​

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