Question 3: Image Orientation Through Mirrors
Step-by-Step Analysis
We trace the orientation of the arrow vector through each reflection.
1. Mirror A (Deflects Light 90° Down):
Object is Vertical Up ($\uparrow$). The mirror is inclined at $45^\circ$. A vertical object reflected in a $45^\circ$ mirror results in a horizontal image. Based on the geometry (turning Right-moving light Down), the top of the arrow maps to the Left.
Image 1: Horizontal, pointing Left ($\leftarrow$).
Object is Vertical Up ($\uparrow$). The mirror is inclined at $45^\circ$. A vertical object reflected in a $45^\circ$ mirror results in a horizontal image. Based on the geometry (turning Right-moving light Down), the top of the arrow maps to the Left.
Image 1: Horizontal, pointing Left ($\leftarrow$).
2. Mirror B (Deflects Light 90° Right):
Incident image is $\leftarrow$. The light is traveling Down. The mirror turns the light to the Right. The vector perpendicular to the plane of incidence (the image vector) is rotated $90^\circ$ counter-clockwise in the view plane.
Image 2: Vertical, pointing Up ($\uparrow$).
Incident image is $\leftarrow$. The light is traveling Down. The mirror turns the light to the Right. The vector perpendicular to the plane of incidence (the image vector) is rotated $90^\circ$ counter-clockwise in the view plane.
Image 2: Vertical, pointing Up ($\uparrow$).
3. Mirror C (Deflects Light 90° Up):
Incident image is $\uparrow$. The light is traveling Right. The mirror turns the light Up. This rotation transforms the vertical image vector into a horizontal one aligned with the new direction of “forward”.
Image 3: Horizontal, pointing Right ($\rightarrow$).
Incident image is $\uparrow$. The light is traveling Right. The mirror turns the light Up. This rotation transforms the vertical image vector into a horizontal one aligned with the new direction of “forward”.
Image 3: Horizontal, pointing Right ($\rightarrow$).
4. Mirror D (Deflects Light 90° Right):
Incident image is $\rightarrow$. The light is traveling Up. The mirror turns light to the Right. The image vector is rotated back to vertical.
Image 4: Vertical, pointing Up ($\uparrow$).
Incident image is $\rightarrow$. The light is traveling Up. The mirror turns light to the Right. The image vector is rotated back to vertical.
Image 4: Vertical, pointing Up ($\uparrow$).
Correct Option: (b) $\leftarrow, \uparrow, \rightarrow, \uparrow$