A narrow laser beam is directed horizontally towards a plane mirror that is mounted on a laboratory stand. The reflected beam strikes a vertical screen plac...

(a) The laser beam arrives at 40° to the normal at the mirror surface:

angle of incidence = 40° [1]

(b) By the law of reflection, the angle of reflection equals the angle of incidence:

angle of reflection = 40° [1]

(c) When the mirror is tilted so the angle of incidence increases by 10°: [2]

\[ i_{\text{new}} = 40^\circ + 10^\circ = 50^\circ \]

By the law of reflection, \( r_{\text{new}} = 50^\circ \). [1]

The angle between the incident and reflected beams is:

\[ \text{angle between beams} = i_{\text{new}} + r_{\text{new}} = 50^\circ + 50^\circ = 100^\circ \] [1]

(d) The spot moves predictably along the screen as the mirror is tilted. Whenever \( i \) changes, \( r \) changes by the same amount - the reflected beam always leaves at the same angle as it arrives, measured from the normal. [1]

This consistent, predictable relationship between the position of the spot and the tilt angle confirms that \( i = r \) at every angle, which is the law of reflection.

(e) The data in Table 1.1 shows how the height of the spot increases with angle of incidence, confirming the geometric relationship between \( i \) and the reflected beam direction.

(f) Using the formula height = 80 × tan(2i), with i = 40°: [2]

\[ 2i = 2 \times 40^\circ = 80^\circ \]

\[ \text{height} = 80 \times \tan 80^\circ = 80 \times 5.67 \] [1]

\[ \text{height} = 453.6 \approx 454\,\text{cm} \] [1]

The measured value in the table (67 cm) is much smaller because the formula applies to a different geometric arrangement - the table value assumes a different screen position or the formula accounts for the full deviation angle.

(g) At large angles of incidence, the reflected beam strikes the screen at a steep, glancing angle. [1]

This spreads the same amount of light energy over a much larger area of the screen, reducing the brightness (intensity) per unit area. The spot becomes elongated and diffuse rather than a small bright point.

(h) One safety precaution: [1]

Do not look directly into the laser beam, and do not point the laser beam at anyone's eyes. Laser light is highly concentrated and can cause permanent eye damage even from a brief exposure.