You are provided with a glass block, plane mirror, and optical pins. (i) Place the glass block on a drawing sheet and trace its outline ABCD as shown in the diagram above. (ii) Remove the block, measure and record the width W of the block. (iii) Draw a normal ON to DC at a point about one-quarter the length of DC. (iv) Draw a line making an angle i = 10^\circ with the normal. (v) Replace the block on its outline and mount the plane mirror vertically behind the block such that it makes good contact with the face AB. (vi) Stick two pins \(P_1\) and \(P_2\) on the line MO. (vii) Looking through the face CD, stick two other pins \(P_3\) and \(P_4\) such that they appear to be in a straight line with the images of pins \(P_1\) and \(P_2\) seen through the block. (viii) Join \(P_3\) and \(P_4\) with a straight line and extend it to touch the face CD at O\(^{1}\). (ix)Draw a perpendicular line from the midpoint of OO\(^{1}\) to meet AB at Q. (x) Draw lines OQ, O\(^{1}\)Q and normal O\(^{1}\)N\(^{1}\) produced. (xi) Measure and record \cos\theta, e, and d. (xii) Evaluate m = sin e, and n cos\(\frac{\theta}{2}\) (xii)Repeat the procedure for i = 20^\circ, 30^\circ, 40^\circ and 50. (xiv) Tabulate your readings. (xv) Plot a graph with m on the vertical axis and n on the horizontal axis. (xvi) Determine the slope, s, of the graph and evaluate \cos\theta = 2Ws. (xvii) State two precautions are taken to ensure accurate results. (xviii) Sketch a diagram to show the path of the ray through the glass block when the angle of incidence i = 90^\circ in the experiment above. (xix) A coin lies at the bottom of a tank containing water to a depth of 130cm. If the refractive index of water is 1.3, calculate the apparent displacement of the coin when viewed vertically from above.