The reflecting surface is represented by the equation \[2x={{y}^{2}}\] as shown in the figure. A ray travelling horizontal becomes vertical after reflection. The co-ordinates of the point of incidence are: |
A) (1/2, 1)
B) (1, 1/2)
C) (1/2, 1/2)
D) none
Correct Answer: A
Solution :
\[i+r=90{}^\circ ,\]and\[\angle i=\angle r\] |
\[\therefore \] \[i=45{}^\circ \] |
Also \[i+\theta =90{}^\circ \] |
\[\therefore \] \[\theta =90{}^\circ -i=90{}^\circ -45{}^\circ =45{}^\circ \] |
Given \[{{y}^{2}}=2x\] Or \[2y\frac{dy}{dx}=2\] |
\[\therefore \] \[\frac{dy}{dx}=\frac{1}{y}\] Or \[tan45{}^\circ =\frac{1}{y}\] |
\[\therefore \] \[y=1\] Now \[x=\frac{{{y}^{2}}}{2}=\frac{{{1}^{2}}}{2}=\frac{1}{2}\] |
You need to login to perform this action.
You will be redirected in
3 sec