#$&* course phy 122 2/8 3There are also questions in this document. 020. `Query 18
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Given Solution: `aThe respective indices of refraction for violet and red light in flint glass appear from the given graph to be about 1.665 and 1.620. The speed of light in a medium is inversely proportional to the index of refraction of that medium, so the ratio of the speed of red to violet light is the inverse 1.665 / 1.62 of the ratio of the indices of refraction (red to violet). This ratio is about 1.028, or 102.8%. So the precent difference is about 2.8%. It would also be possible to figure out the actual speeds of light, which would be c / n_red and c / n_violet, then divide the two speeds; however since c is the same in both cases the ratio would end up being c / n_red / ( c / n_violet) = c / n_red * n_violet / c = n_violet / n_red, and the result would be the same as that given above. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): After reading the explanation, I think that I understand the problem. ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q **** query gen phy problem 24.34 width of 1st-order spectrum of white light (400 nm-750nm) at 2.3 m from a 7500 line/cm grating **** gen phy what is the width of the spectrum? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The spectrum is from 400 nm-750 nm. The screen is 2.3 m away and that the grating is 7500 lines/cm. Sin of theta= m x wavelength / d These are first order angles m will be 1 Since the grating is 7500 lines/cm, d will be 1/7500 cm or 1/750000m Sin of theta (400nm)=1 *(4.0*10^-7)/1/75000 Sin of theta (400nm)=0.300 Theta( 400nm)=17.46 degrees This is the angle that the first order 400 nm ray will make Sin of theta 750 nm= 0.563 Theta(750 nm)=34.24 degrees This is the angle that the first order 750 nm ray will make. Tan of theta= opp/adjacent Tan of 34.24 degrees=opp/2.3 m 0.6806=opp/2.3 Opp=1.57m Tan of 17.46=opp/2.3 Opp=0.72 So from point A to where the angle (400 nm) hits the screen is 0.72 meters From point A to where the angle (750 nm) hits the screen is 1.57 m Spectrum width : 2.3 m * tan (31.33) - 2.3m x tan(17.45)=0.68m The spectrum will be 1.57-.72= .85 m wide confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Terrible. I still can’t figure out how to find the angle.
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Given Solution: `aGOOD STUDENT SOLUTION We are given that the spectrum is from 400-750 nm. We are also given that the screen is 2.3 meters away and that the grating is 7500 lines/cm. To find this I will find where 400 nm wavelength falls on the screen and also where 750 nm wavelength falls onto the screen. Everything in between them will be the spectrum. I will use the formula... sin of theta = m * wavelength / d since these are first order angles m will be 1. since the grating is 7500 lines/cm, d will be 1/7500 cm or 1/750000 m. Sin of theta(400nm) = 1 * (4.0 * 10^-7)/1/750000 sin of theta (400nm) = 0.300 theta (400nm) = 17.46 degrees This is the angle that the 1st order 400nm ray will make. sin of theta (750nm) = 0.563 theta (750nm) = 34.24 degrees This is the angle that the 1st order 750 nm ray will make. We were given that the screen is 2.3 meters away. If we draw an imaginary ray from the grating to to the screen and this ray begins at the focal point for the rays of the spectrum and is perpendicular to the screen (I will call this point A), this ray will make two triangles, one with the screen and the 400nm angle ray and one with the screen and the 750 nm angle ray. Using the trigonomic function; tangent, we can solve for the sides of the triangles which the screen makes up. Tan of theta = opposite / adjacent tan of 34.24 degrees = opposite / 2.3 meters 0.6806 = opposite / 2.3 meters opposite = 1.57 meters tan of 17.46 degrees = opposite / 2.3 meters opposite = 0.72 meters So from point A to where the angle(400nm) hits the screen is 0.72 meters. And from point A to where the angle(750nm) hits the screen is 1.57 meters. If you subtract the one segment from the other one you will get the length of the spectrum on the screen. 1.57 m - 0.72 m = 0.85 meters is the width of the spectrum on the screen. CORRECTION ON LAST STEP: spectrum width = 2.3m * tan (31.33)) - 2.3m * tan (17.45) = 0.68m STUDENT QUESTION: 1.57-.72 = 0.85m. Why subtract? INSTRUCTOR RESPONSE We're finding the distance from the 400 nm light on the screen (the violet end of the spectrum), which reinforces at about 17 deg, to the 750 nm light (the red end), which reinforces at 34 deg. At the given distance the grating will produce a ROY G BIV spectrum from violet to red, spread out from a point .72 m from the center of the pattern, to a point 1.57 m from the center. The spectrum will therefore be 1.57 m - .72 m = .85 m wide. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): Professor, I know that there is lots of detail above about how to solve this problem, but I still don’t understand how to determine the angle. Would you mind to provide LOTS of detail of how I will solve for the angle? When I use tangent function, do I just plug that into my calculator? Any assistance that you can provide, would be most appreciated! " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: ********************************************* Question: `q **** query gen phy problem 24.34 width of 1st-order spectrum of white light (400 nm-750nm) at 2.3 m from a 7500 line/cm grating **** gen phy what is the width of the spectrum? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The spectrum is from 400 nm-750 nm. The screen is 2.3 m away and that the grating is 7500 lines/cm. Sin of theta= m x wavelength / d These are first order angles m will be 1 Since the grating is 7500 lines/cm, d will be 1/7500 cm or 1/750000m Sin of theta (400nm)=1 *(4.0*10^-7)/1/75000 Sin of theta (400nm)=0.300 Theta( 400nm)=17.46 degrees This is the angle that the first order 400 nm ray will make Sin of theta 750 nm= 0.563 Theta(750 nm)=34.24 degrees This is the angle that the first order 750 nm ray will make. Tan of theta= opp/adjacent Tan of 34.24 degrees=opp/2.3 m 0.6806=opp/2.3 Opp=1.57m Tan of 17.46=opp/2.3 Opp=0.72 So from point A to where the angle (400 nm) hits the screen is 0.72 meters From point A to where the angle (750 nm) hits the screen is 1.57 m Spectrum width : 2.3 m * tan (31.33) - 2.3m x tan(17.45)=0.68m The spectrum will be 1.57-.72= .85 m wide confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Terrible. I still can’t figure out how to find the angle.
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Given Solution: `aGOOD STUDENT SOLUTION We are given that the spectrum is from 400-750 nm. We are also given that the screen is 2.3 meters away and that the grating is 7500 lines/cm. To find this I will find where 400 nm wavelength falls on the screen and also where 750 nm wavelength falls onto the screen. Everything in between them will be the spectrum. I will use the formula... sin of theta = m * wavelength / d since these are first order angles m will be 1. since the grating is 7500 lines/cm, d will be 1/7500 cm or 1/750000 m. Sin of theta(400nm) = 1 * (4.0 * 10^-7)/1/750000 sin of theta (400nm) = 0.300 theta (400nm) = 17.46 degrees This is the angle that the 1st order 400nm ray will make. sin of theta (750nm) = 0.563 theta (750nm) = 34.24 degrees This is the angle that the 1st order 750 nm ray will make. We were given that the screen is 2.3 meters away. If we draw an imaginary ray from the grating to to the screen and this ray begins at the focal point for the rays of the spectrum and is perpendicular to the screen (I will call this point A), this ray will make two triangles, one with the screen and the 400nm angle ray and one with the screen and the 750 nm angle ray. Using the trigonomic function; tangent, we can solve for the sides of the triangles which the screen makes up. Tan of theta = opposite / adjacent tan of 34.24 degrees = opposite / 2.3 meters 0.6806 = opposite / 2.3 meters opposite = 1.57 meters tan of 17.46 degrees = opposite / 2.3 meters opposite = 0.72 meters So from point A to where the angle(400nm) hits the screen is 0.72 meters. And from point A to where the angle(750nm) hits the screen is 1.57 meters. If you subtract the one segment from the other one you will get the length of the spectrum on the screen. 1.57 m - 0.72 m = 0.85 meters is the width of the spectrum on the screen. CORRECTION ON LAST STEP: spectrum width = 2.3m * tan (31.33)) - 2.3m * tan (17.45) = 0.68m STUDENT QUESTION: 1.57-.72 = 0.85m. Why subtract? INSTRUCTOR RESPONSE We're finding the distance from the 400 nm light on the screen (the violet end of the spectrum), which reinforces at about 17 deg, to the 750 nm light (the red end), which reinforces at 34 deg. At the given distance the grating will produce a ROY G BIV spectrum from violet to red, spread out from a point .72 m from the center of the pattern, to a point 1.57 m from the center. The spectrum will therefore be 1.57 m - .72 m = .85 m wide. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): Professor, I know that there is lots of detail above about how to solve this problem, but I still don’t understand how to determine the angle. Would you mind to provide LOTS of detail of how I will solve for the angle? When I use tangent function, do I just plug that into my calculator? Any assistance that you can provide, would be most appreciated! " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&! ********************************************* Question: `q **** query gen phy problem 24.34 width of 1st-order spectrum of white light (400 nm-750nm) at 2.3 m from a 7500 line/cm grating **** gen phy what is the width of the spectrum? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: The spectrum is from 400 nm-750 nm. The screen is 2.3 m away and that the grating is 7500 lines/cm. Sin of theta= m x wavelength / d These are first order angles m will be 1 Since the grating is 7500 lines/cm, d will be 1/7500 cm or 1/750000m Sin of theta (400nm)=1 *(4.0*10^-7)/1/75000 Sin of theta (400nm)=0.300 Theta( 400nm)=17.46 degrees This is the angle that the first order 400 nm ray will make Sin of theta 750 nm= 0.563 Theta(750 nm)=34.24 degrees This is the angle that the first order 750 nm ray will make. Tan of theta= opp/adjacent Tan of 34.24 degrees=opp/2.3 m 0.6806=opp/2.3 Opp=1.57m Tan of 17.46=opp/2.3 Opp=0.72 So from point A to where the angle (400 nm) hits the screen is 0.72 meters From point A to where the angle (750 nm) hits the screen is 1.57 m Spectrum width : 2.3 m * tan (31.33) - 2.3m x tan(17.45)=0.68m The spectrum will be 1.57-.72= .85 m wide confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Terrible. I still can’t figure out how to find the angle.
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Given Solution: `aGOOD STUDENT SOLUTION We are given that the spectrum is from 400-750 nm. We are also given that the screen is 2.3 meters away and that the grating is 7500 lines/cm. To find this I will find where 400 nm wavelength falls on the screen and also where 750 nm wavelength falls onto the screen. Everything in between them will be the spectrum. I will use the formula... sin of theta = m * wavelength / d since these are first order angles m will be 1. since the grating is 7500 lines/cm, d will be 1/7500 cm or 1/750000 m. Sin of theta(400nm) = 1 * (4.0 * 10^-7)/1/750000 sin of theta (400nm) = 0.300 theta (400nm) = 17.46 degrees This is the angle that the 1st order 400nm ray will make. sin of theta (750nm) = 0.563 theta (750nm) = 34.24 degrees This is the angle that the 1st order 750 nm ray will make. We were given that the screen is 2.3 meters away. If we draw an imaginary ray from the grating to to the screen and this ray begins at the focal point for the rays of the spectrum and is perpendicular to the screen (I will call this point A), this ray will make two triangles, one with the screen and the 400nm angle ray and one with the screen and the 750 nm angle ray. Using the trigonomic function; tangent, we can solve for the sides of the triangles which the screen makes up. Tan of theta = opposite / adjacent tan of 34.24 degrees = opposite / 2.3 meters 0.6806 = opposite / 2.3 meters opposite = 1.57 meters tan of 17.46 degrees = opposite / 2.3 meters opposite = 0.72 meters So from point A to where the angle(400nm) hits the screen is 0.72 meters. And from point A to where the angle(750nm) hits the screen is 1.57 meters. If you subtract the one segment from the other one you will get the length of the spectrum on the screen. 1.57 m - 0.72 m = 0.85 meters is the width of the spectrum on the screen. CORRECTION ON LAST STEP: spectrum width = 2.3m * tan (31.33)) - 2.3m * tan (17.45) = 0.68m STUDENT QUESTION: 1.57-.72 = 0.85m. Why subtract? INSTRUCTOR RESPONSE We're finding the distance from the 400 nm light on the screen (the violet end of the spectrum), which reinforces at about 17 deg, to the 750 nm light (the red end), which reinforces at 34 deg. At the given distance the grating will produce a ROY G BIV spectrum from violet to red, spread out from a point .72 m from the center of the pattern, to a point 1.57 m from the center. The spectrum will therefore be 1.57 m - .72 m = .85 m wide. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): Professor, I know that there is lots of detail above about how to solve this problem, but I still don’t understand how to determine the angle. Would you mind to provide LOTS of detail of how I will solve for the angle? When I use tangent function, do I just plug that into my calculator? Any assistance that you can provide, would be most appreciated! " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!#*&!