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(1) A lens made of glass (with index of refraction n g = 1.53) is coated witht a thin film of ITO (with index of refraction n s = 2.00) of thickness t. Visible light of wavelength 450 nm (in air) is incident normally on the coated lens as in Fig. B11. (8 marks) ITO (a) Determine the wavelength and frequency of the light in the ITO layer. (2 marks) (b) For what minimum value of t will the reflected light be missing? (4 marks) (c) Are there other values of t that will minimize the reflected light at this wavelength? If yes, write down 2 other values of t. If no, explain. (2 marks) any integer of multiples of 112.5nm, e.g. 225 nm (m=2), 337.5 nm (m=3), etc. m = 1 225 ( ) 2 450 nm n n
- 67 10 ( ) 450 10 (^3 ) 9 8 Hz c f f (^)
2 nt m ( m 1 , 2 , 3 ,...)
nm
n
t
by lens formula, p 1 = 40 cm, f 1 = 20 cm q 1 = 40 cm p 2 = 30 – 40 = -10 cm, f 2 = 10 cm q 2 = 5 cm Therefore final image is 5 cm to the right of the 2 nd^ lens M = (-q 1 /p 1 ) (-q 2 /p 2 ) = (-40/40)(-5/-10) =-0. the image is inverted (2) An object is located 40 cm from the first of two thin converging lenses of focal lengths 20 cm and 10 cm, respectively (Fig. A1). The lenses are separated by 30 cm. Determine the location and the lateral magnification of the final image formed by the two-lens system. State whether the final image is upright or inverted. (5 marks)
- p
(3) The lens and mirror in Fig. Q9 are separated by d = 1.00 m and have focal lengths of 80. cm and 50.0 cm, respectively. An object is placed p =1.00 m to the left of the lens. Note that the first image produced by the lens will be the object for the mirror, and that the image produced by the mirror will be the second object for the lens. (d) Find the image distance of the second image (i.e. the final image) produced by the lens. (2 marks) The image formed by the mirror is 100 cm + 60 cm = 160 cm to the right of the lens. Therefore, for the second pass through the lens, p 3 = 160 cm. 1/q 3 = 1/f 1 – 1/p 3 , f 1 = 80 cm, p 3 = 160 cm, so q 3 = 160 cm, i.e. 160 cm to the left of the mirror. (e) Determine the overall magnification of the image. (2 marks) (f) State whether the final image is upright or inverted, real or virtual. (2 marks) (g) State the two typical types of lens aberrations. (2 marks) Since M < 0, the final image is inverted, real M 1 = - q 1 /p 1 = -400 cm / 100 cm = -4.00, M 2 = - q 2 /p 2 = - (-60.0 cm) / (-300 cm) = -1/ M 3 = - q 3 /p 3 = -160 cm / 160 cm = -1.00, M = M 1 M 2 M 3 = -0. Spherical aberration and chromatic aberration
min = 1.22 λ/D =1.22 x 579 x 10-9^ m / (1.2 x 10-2^ m) = 5.89 x 10-5^ rad (5) Light of wavelength 579 nm is used to view an object under a microscope. Suppose that the aperture of the objective has a diameter of 1.2 cm. (5 marks) (a) Calculate the angular resolution of the microscope. (2 marks) (b) Suppose that water (n = 1.33) fills the space between the object and objective. What is the resolving angle when 579 nm light is used? Suggest whether the resolving power is improved in this case. (3 marks) water = air / nwater = 579 x 10-9^ m /1.33 = 435 nm min = 1.22 λ/D =1.22 x 435 x 10
- m / (1.2 x 10 - m) = 4.43 x 10 - rad Yes, the resolving power is improved.
(6) Blue light of wavelength 470 nm is incident normally to a diffraction grating ruled 5000 lines per cm. (7 marks) (a) Calcualte the angular deviation of the 2 nd order maximum from the central maximum. (3 marks) (b) What is the highest-order image that can be viewed through this grating at this wavelength of light? (4 marks) θ = 28° For maximum order of viewing n, the limiting value of θ is 90° n < 4. thereofer maximum viewing order is 4.
n = 1/sin (48. o ) = 1. (8) The critical angle of total internal reflection for a particular material is 48.6°. (5 marks) (a) Calculate the refractive index of the material. (2 marks) (b) Calculate the polarizing angle for light striking on the same material. (3 marks) tan p = nair / n = 1/1. p = 36. o
