WBJEE · Physics · Ray Optics
If \(\hat{n}_1, \hat{n}_2\) and \(\hat{t}\) represent, unit vectors along the incident ray, reflected ray and normal to the surface respectively, then
- A \(\quad \hat{n}_2=\hat{n}_1-2\left(\hat{n}_1 \cdot \hat{t}\right) \hat{\mathrm{t}}\)
- B \(\hat{n}_2=\hat{n}_1+2\left(\hat{n}_1 \cdot \hat{t}\right) \hat{\mathrm{t}}\)
- C \(\hat{n}_2=-\hat{n}_1\)
- D \(\hat{n}_2=2 \hat{n}_1-\left(\hat{n}_1 \times \hat{t}\right) \cdot \hat{n}_1\)
Answer & Solution
Correct Answer
(A) \(\quad \hat{n}_2=\hat{n}_1-2\left(\hat{n}_1 \cdot \hat{t}\right) \hat{\mathrm{t}}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Hint: } \hat{n}_1=-\cos \theta \hat{\mathrm{t}}+\sin \theta \hat{\mathrm{i}} \\ & \hat{\mathrm{n}}_2=\cos \theta \hat{\mathrm{t}}+\sin \theta \hat{\mathrm{i}} \\ & \hat{\mathrm{n}}_2-\hat{\mathrm{n}}_1=2 \cos \theta \hat{\mathrm{t}}=-2(\hat{\mathrm{n}}…
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