What Is The Focal Length (In M) Of A Makeup Mirror That Has A Power Of 1.02 D?

The Mirror Equation - Convex Mirrors

Ray diagrams tin can be used to make up one's mind the image location, size, orientation and type of image formed of objects when placed at a given location in front end of a mirror. The employ of these diagrams was demonstrated earlier in Lesson 3 and in Lesson 4. Ray diagrams provide useful information well-nigh object-paradigm relationships, yet fail to provide the data in a quantitative course. While a ray diagram may help ane determine the approximate location and size of the image, it will not provide numerical information nearly image distance and epitome size. To obtain this type of numerical information, it is necessary to utilise the Mirror Equation and the Magnification Equation . The mirror equation expresses the quantitative human relationship betwixt the object altitude (d_o), the image distance (d_i), and the focal length (f). The equation is stated as follows:

The magnification equation relates the ratio of the prototype altitude and object distance to the ratio of the image height (h_i) and object acme (h_o). The magnification equation is stated as follows:

These two equations can exist combined to yield information virtually the image distance and epitome pinnacle if the object distance, object height, and focal length are known. Their use was demonstrated in Lesson 3 for concave mirrors and volition be demonstrated hither for convex mirrors. Equally a demonstration of the effectiveness of the Mirror equation and Magnification equation, consider the following example problem and its solution.

Instance Trouble #1

A 4.0-cm tall light bulb is placed a altitude of 35.v cm from a convex mirror having a focal length of -12.2 cm. Make up one's mind the image distance and the prototype size.

Similar all problems in physics, begin by the identification of the known information.

ho = 4.0 cm

do = 35.five cm

f = -12.2 cm

Next identify the unknown quantities that you wish to solve for.

To make up one's mind the epitome altitude (d_i), the mirror equation will have to be used. The following lines stand for the solution to the image altitude; substitutions and algebraic steps are shown.

ane/f = one/do + 1/d_i

ane/(-12.2 cm) = 1/(35.5 cm) + 1/d_i

-0.0820 cm^-ane = 0.0282 cm^-1 + i/d_i

-0.110 cm^-ane = 1/d_i

The numerical values in the solution above were rounded when written down, yet unrounded numbers were used in all calculations. The final answer is rounded to the tertiary significant digit.

To determine the epitome pinnacle (h_i), the magnification equation is needed. Since three of the four quantities in the equation (disregarding the M) are known, the fourth quantity tin be calculated. The solution is shown below.

h_i/h_o = - d_i/d_o

h_i /(4.0 cm) = - (-9.08 cm)/(35.five cm)

h_i = - (four.0 cm) • (-nine.08 cm)/(35.5 cm)

The negative values for prototype altitude indicate that the image is located behind the mirror. Equally is frequently the case in physics, a negative or positive sign in forepart of the numerical value for a physical quantity represents information well-nigh direction. In the case of the paradigm distance, a negative value always indicates the existence of a virtual image located behind the mirror. In the case of the prototype height, a positive value indicates an upright image. Further data about the sign conventions for the variables in the Mirror Equation and the Magnification Equation tin be found in Lesson iii.

From the calculations in this trouble it tin can exist concluded that if a 4.0-cm tall object is placed 35.v cm from a convex mirror having a focal length of -12.ii cm, then the image will be upright, ane.02-cm alpine and located 9.08 cm behind the mirror. The results of this calculation hold with the principles discussed before in this lesson. Convex mirrors always produce images that are upright, virtual, reduced in size, and located behind the mirror.

We Would Like to Suggest ...

Why only read about information technology and when you could be interacting with it? Interact - that's exactly what you practise when you utilise one of The Physics Classroom's Interactives. We would similar to propose that you combine the reading of this folio with the utilise of our Optics Bench Interactive or our Name That Prototype Interactive. You tin find this in the Physics Interactives section of our website. The Optics Bench Interactive provides the learner an interactive enivronment for exploring the germination of images by lenses and mirrors. The Name That Paradigm Interactive provides learners with an intensive mental conditioning in recognizing the image characteristics for any given object location in forepart of a curved mirror.

Cheque Your Understanding

1. A convex mirror has a focal length of -10.8 cm. An object is placed 32.vii cm from the mirror'due south surface. Determine the prototype altitude.

2. Determine the focal length of a convex mirror that produces an prototype that is 16.0 cm behind the mirror when the object is 28.5 cm from the mirror.

iii. A 2.80-cm diameter money is placed a altitude of 25.0 cm from a convex mirror that has a focal length of -12.0 cm. Determine the image distance and the diameter of the paradigm.

four. A focal point is located 20.0 cm from a convex mirror. An object is placed 12 cm from the mirror. Determine the epitome distance.

Source: https://www.physicsclassroom.com/class/refln/Lesson-4/The-Mirror-Equation-Convex-Mirrors

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