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21) In figure (a) at the right, a glass lens (n> 1) has a flat top surface and a spherical bottom surface with radius of curvature R. The bottom surface of the lens sits on a flat glass plate (n > 1). In air above the lens, light with wavelength in air is incident perpendicularly onto the top surface of the lens. Figure (b) at the right shows a photo taken from above, looking down through the lens. In the photo, we can see circular bright and dark rings (called Newton's rings) caused by interference of the reflected light due to the varying thickness of the thin film of air between the lens and the plate. a) (i) Show that radii r of the bright rings (interference maxima) Incident light Glass Air Glass (a) are given by the equation r=R²- ma R- 4 where m=1,3,5,..., assuming that r << R. (ii) Show that, because |Rm2 1<

21) In figure (a) at the right, a glass lens (n> 1) has a flat top surface and a spherical bottom surface with radius of curvature R. The bottom surface of the lens sits on a flat glass plate (n > 1). In air above the lens, light with wavelength in air is incident perpendicularly onto the top surface of the lens. Figure (b) at the right shows a photo taken from above, looking down through the lens. In the photo, we can see circular bright and dark rings (called Newton's rings) caused by interference of the reflected light due to the varying thickness of the thin film of air between the lens and the plate. a) (i) Show that radii r of the bright rings (interference maxima) Incident light Glass Air Glass (a) are given by the equation r=R²- ma R- 4 where m=1,3,5,..., assuming that r << R. (ii) Show that, because |Rm2 1<

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21) In figure (a) at the right, a glass lens (n> 1) has a flat top surface and a spherical bottom surface with radius of curvature R. The bottom surface of the lens sits on a flat glass plate (n > 1). In air above the lens, light with wavelength 2 in air is incident perpendicularly onto the top surface of the lens. Figure (b) at the right shows a photo taken from above, looking down through the lens. In the photo, we can see circular bright and dark rings (called Newton's rings) caused by interference of the reflected light due to the varying thickness of the thin film of air between the lens and the plate. a) (i) Show that radii r of the bright rings (interference maxima) Incident light Glass Air Glass (a) are given by the equation r=R²- ma R- where 4 m=1,3,5,..., assuming that r << R. (ii) Show that, because Rm1 1<< R, this reduces to r=, 2
Transcribed Image Text:21) In figure (a) at the right, a glass lens (n> 1) has a flat top surface and a spherical bottom surface with radius of curvature R. The bottom surface of the lens sits on a flat glass plate (n > 1). In air above the lens, light with wavelength 2 in air is incident perpendicularly onto the top surface of the lens. Figure (b) at the right shows a photo taken from above, looking down through the lens. In the photo, we can see circular bright and dark rings (called Newton's rings) caused by interference of the reflected light due to the varying thickness of the thin film of air between the lens and the plate. a) (i) Show that radii r of the bright rings (interference maxima) Incident light Glass Air Glass (a) are given by the equation r=R²- ma R- where 4 m=1,3,5,..., assuming that r << R. (ii) Show that, because Rm1 1<< R, this reduces to r=, 2
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Proved り RP - (R?
Transcribed Image Text:Proved り RP - (R?
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