Question

In: Physics

ESSAY PART: A group of students of students wants to build an apparatus that produces a...

ESSAY PART:

A group of students of students wants to build an apparatus that produces a mirage of an object. For this purpose, they need to know the radius of curvature of the concave mirror they are using. Please explain how they can achieve their goal? Make sure to indicate variables, equipment necessary and possible procedure. (10pts) Also on the space labeled Experimental setup sketch your apparatus.

Experimental Setup: (5 pts)

  1. The students completed their corresponding measurements and obtained the following data:

Distance to the object (cm)

10

15

20

25

30

35

Distance to the image (m)

30

15

12

10.7

10

9.5

Complete the above table by manipulating the data so that you are able to determine the focal length of the mirror. (20pts)

  1. Graph your manipulated data. (20 pts)

  1. Write the mathematical equation describing the relationship. Explain the physical meaning of the slope and the y-intercept. (30 pts)

Mathematical Equation: ____________________    Meaning of the Slope:             Meaning of the y-intercept:

  1. Determine the radius of curvature of the mirror: (5 pts)
  2. The mirror has a radius of curvature of 14.8 cm. Determine the percentage error of the experiment. (5 pts)

Solutions

Expert Solution

Distance to Object u (cm) 10 15 20 25 30 35
Distance to image v ( cm ) 30 15 12 10.7 10 9.5
Reciprocal of distance to Object , 1/u ( cm-1) 0.1 0.067 0.05 0.04 0.033 0.029
Reciprocal of distance to Image , 1/v ( cm-1) 0.033 0.067 0.083 0.093 0.1 0.105

We have mirror equation :- (1/v) + (1/u) = (1/f)

where f is focal length of mirror

Hence get, (1/v) = -(1/u) + (1/f)   ................(1)

From eqn.(1), we see that if we use (1/v) as ordinate ( y-variable) and (1/u) as abscissa ( x-variable)

we have linear equation.

Slope of graph of linear equation is -1 and y intercept of graph of linear equation is

reciprocal of focal length of concave mirror.

Radius of curvature of concave mirror = twice of focal length

Graph shown above is plotted using excel using (1/u) and (1/v) values

Trendline equation ( linear ) is shown in the graph.

y-intercept = reciprocal of focal length 1/f = 0.133 cm-1

focal length = 1/0.133 = 7.52 cm

Radius of curvature = 15.04 cm

If actual radius of curvature is 14.8 cm , then % error = [ (15.04 -14.8) / 14.8 ] 100 1.61

genius_generous answered 8 months ago
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