Hi dear I need help plz. i would really appreciate if you show work answers and explanation even in the multiple choice questions

21d. [4 marks] Monochromatic light of wavelength 633 nm is normally incident on a diffraction grating. The diffraction maxima incident on a screen are detected and their angle 0 to the central beam is determined. The graph shows the variation of sino with the order n of the maximum. The central order corresponds to n = 0. 0.45- 0.4 0.35 0.3 0.25 sin 0 0.2 0.15- 0.1- 0.05- n Determine a mean value for the number of slits per millimetre of the grating. . . . . . .. . ....'' . . . .. .. ".. .. .. . . . . . . . . . . . . .. . .... ... ..21e. [1 mark] State the effect on the graph of the variation of sin 0 with n of: using a light source with a smaller wavelength. . . . . . . ... . . . . . . .... 21f. [1 mark] increasing the distance between the diffraction grating and the screen. . . . . . . . . . . . .. . . . . . . . . . .21a. [1 mark] Monochromatic light of wavelength A is normally incident on a diffraction grating. The diagram shows adjacent slits of the diffraction grating labelled V, W and X. Light waves are diffracted through an angle 0 to form a second-order diffraction maximum. Points Z and Y are labelled. X d A W d State the phase difference between the waves at V and Y. 21b. [1 mark] State, in terms of 1, the path length between points X and Z. . . . ....... . . . .. ....... 21c. [1 mark] The separation of adjacent slits is d. Show that for the second-order diffraction maximum 22 = dsin 0,What is the speed of the surfboard and what is the direction of motion of the surfboard relative to the beach? wave direction girl on surfboard Speed of surfboard Direction of motion of relative to the beach / m5\" surfboard relative to the beach A. 6.0 towards beach B. 60 away from beach C, 175 towards beach D, 15 away from beach 16. [1 mark] A simple pendulum and a massspring system oscillate with the same time period. The mass of the pendulum hob and the mass on the spring are initially identical. The masses are halved. What is A\"? z 3.1 ex/E 0.2 time period of pendulum time period of massspring system when the masses have been changed? 20a. [2 marks] The lens of an optical system is coated with a thin film of magnesium fluoride of thickness d. Monochromatic light of wavelength 656 nm in air is incident on the lens. The angle of incidence is 0. Two reflected rays, X and Y, are shown. magnesium fluoride d lens do The following refractive indices are available. Air = 1.00 Magnesium fluoride = 1.38 Lens = 1.58 Predict whether reflected ray X undergoes a phase change. 20b. [1 mark] The thickness of the magnesium fluoride film is d. For the case of normal incidence (0 = 0), state, in terms of d, the path difference between the reflected rays X and Y. 20c, [2 marks] calculate the smallest value of d that will result in destructive interference between ray X and ray Y.11. [1 mark] A train is approaching an observer with constant speed 34 where c is the speed of sound in still air. The train emits sound of wavelength 2. What is the observed speed of the sound and observed wavelength as the train approaches? Speed of sound Wavelength A. 337 C 34 B. 35c 332 34 34 C. C 2 D 35c 34 2 12. [1 mark] An object undergoes simple harmonic motion (shm) of amplitude xo. When the displacement of the object is ~, the speed of the object is v. What is the speed when the displacement is xo? A. 0 C. YZ V D. 3017. [1 mark] Light is incident on a diffraction grating. 1The vlyageslglagr'g: E}; 2:; 253:? a; :2: :31]; differ by 0.5911711 and have a mean wave engt 0- .' ' . ' . resolved in the fourth order of the grating. What IS the minimum number of grating lm that were illuminated? A. 25 B. 250 C. 1000 D. 4000 18. [1 mark] White light is incident normally on separate diffraction gratings X and Y. Y has a greater number of lines per metre than X. Three statements about differences between X and Yare 1. adjacent slits in the gratings are further apart for X than for Y 11. the angle between red and blue light in a spectral order is greater in X than in Y 111. the total number of Visible orders is greater for X than for Y. Which statements are correct? j A. landllonly B. land 1]] only C. II and III only D. I, II and Ill 20d. [2 marks] discuss a practical advantage of this arrangement. 20e. [2 marks] Light from a point source is incident on the pupil of the eye of an observer. The diameter of the pupil is 2.8 mm. Draw, on the axes, the variation with diffraction angle of the intensity of light incident on the retina of the observer. Intensity > Diffraction angle 20f. [2 marks] Estimate in rad, the smallest angular separation of two distinct point sources of light of wavelength 656 nm that can be resolved by the eye of this observer