Determination of the Angle of Minimum Deviation

Determination of the Angle of Minimum Deviation for a given Prism

Aim

To determine angle of minimum deviation for a given prism by plotting a graph between angle of incidence and angle of deviation.

Apparatus and Material Required

• Drawing board,
• triangular glass prism,
• metre scale,
• alpins,
• cellotape/drawing pins,
• graph paper,
• protractor,
• white paper sheets.

Principle

A triangular prism consists of three rectangular lateral surfaces and two triangular bases. The two lateral surfaces, through which light ray is traced, are refracting surfaces. The angle between the two is \(\textbf{angle of the prism}\).

A ray of light \(PQ\) is incident on the first face \(AB\) of the prism of refractive index \(n_2\) from air \(n_1 \simeq 1\). The angle of incidence is \(i\). Light ray bends along \(QR\) and falls on the other face \(AC\) of the prism. The angle of incidence for this glass-air interface is \(r’\). Finally, the ray emerges as \(RS\). The angle of refraction at this face is \(r\).

\(\textbf{Angle of Deviation}\) is the angle by which the ray passing through an optical media deviates from its path. Here, the angle between the incident ray \(PQ\) (produced forward) and the emergent ray \(RS\) (produced backward) is teh angle of deviation, \(\delta\).

From geometrical considerations, we have \[r+r’ = A\]\[\delta = (i-r) + (e-r’) = i+e – A\]

At the position of the prism for minimum deviation \(\delta_m\), the light ray passes through the prism symmetrically, i.e. parallel to the base so that when \[\delta = \delta_m , i =e \text{ which implies } r =r’ \]

The advantage of putting the prism in minimum deviation position is that the image is brightest in this position.

Procedure

1. Fix a white sheet of paper on a drawing board with the help of cellotape or drawing pins.
2. Draw a straight line XY, using a sharp pencil nearly in the middle and parallel to the length of the paper.
3. Mark points \(O_1\), \(O_2\), \(O_3\)… on the straight line XY at suitable distances of about 8 to 10 cm and draw normals \(O_1N_1\), \(O_2N_2\), \(O_3N_3\)… on these points.
4. Draw straight lines \(P_1O_1\), \(P_2O_2\), \(P_3O_3\)… corresponding to the incident rays making angles of incidence at 35°, 40°, 45°… respectively.
5. Place the prism with its refracting face AB on the line XY with point \(O_1\) in the middle of AB as shown in the figure. Draw the boundary of the prism with a sharp pencil.
6. Fix two alpins \(P_1\) and \(Q_1\) with sharp tips vertically about 10 cm apart, on the incident ray line \(P_1Q_1\) such that pin \(Q_1\) is close to point \(O_1\). Close one eye (say left) and looking through the prism, bring your right eye in line with the images of the pins \(P_1\) and \(Q_1\). Fix alpins \(R_1\) and \(S_1\) about 10 cm apart vertically on the white paper sheet with their tips in line with the tips of the images of pins \(P_1\) and \(Q_1\). In this way pins \(R_1\) and \(S_1\) will become collinear, with the images of pins \(P_1\) and \(Q_1\).
7. Remove the pins \(R_1\) and \(S_1\) and encircle their pin pricks on the white paper sheet with the help of a sharp pencil. Remove the pins \(P_1\) and \(Q_1\) and encircle their pin pricks also.
8. Join the points ( or pin pricks) \(R_1\) and \(S_1\) to obtain the emergent ray \(R_1S_1\) . Produce it backwards to meet the incident ray \(P_1Q_1\)(produced forward) at \(T_1\).
9. Measure the angle of deviation \(\delta_1\) and the angle BAC (angle A) of the prism.
10. Repeat steps 5 to 9 for different values of angle of incidence and measure the angle of deviations for each of them.
11. Record observations in tabular form.

Observations

Least count of the protractor =1 (degree)

Angle of the prism, A = 60 (degree)

Plotting Graph

Plotting the graph between \(i\) and \(\delta\) for Determination of the Angle of Minimum Deviation for a given Prism

Take angle of incidence \(i\) along x-axis and angle of deviation \(\delta\) along
y-axis. Choose suitable scales on these axes and plot a graph between \(i\) and \(\delta\). Take care that you draw a free hand smooth curve passing practically through all the plotted points on the graph.

Calculations

Draw tangent on the lowest point of the graph parallel to x-axis, read the angle of minimum deviation \(\delta_m\) on the y-axis of the graph.

Results

Angle of minimum deviation, \(\delta_m\) = degree

Precautions

• Fix alpins vertically to the plane of paper.
• Distance PQ and RS should be about 10 cm in order to locate incident and emergent rays with greater accuracy.
• Same angle of prism should be used for all observations.
• Position of the prism should not be disturbed for a given set of observations.

Sources of errors

• Incorrect way of measuring angles.
• The pins on emergent ray are not collinear with those on incident rays.

Conclusion

The experiment confirms that the angle of deviation decreases with increasing incidence angle, reaches a minimum, and then rises. The plotted graph forms a “V” shape, with the lowest point representing the angle of minimum deviation.

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Reference: NCERT Lab Manual

Determination of the Angle of Minimum Deviation for a given Prism