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Question: 1. What is the magnification equation?2. What is the purpose for the eye-piece in the lens combination?3. Given an object distance of 41[mm] and a thin-lens focal length of 162[mm], then what is the image distance?4. What is the scale factor (M) of the image seen in the previous question?–Free Chegg Question Answer

1. What is the magnification equation?
– Magnification = -qp-1
– Magnification = -pq-1
– Magnification = 1/f + 1/q
– Magnification = 1/q + 1/p
– Magnification = qp-1
– Magnification = -qp-2


2. What is the purpose for the eye-piece in the lens combination?
– The objective takes eye-piece’s real image and creates a magnified real image.
– The eye-piece takes the real object and creates a virtual image.
– The eye-piece takes the objective’s real image and creates a magnified virtual image.
– The eye-piece takes the objective’s real image and creates a magnified real image.

3. Given an object distance of 41[mm] and a thin-lens focal length of 162[mm], then what is the image distance?

4. What is the scale factor (M) of the image seen in the previous question?

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General guidance

Concepts and reason

The concept used here to solve the problem, is the properties of thin lenses.

Further, use lens formula to calculate the image distance using the given values of focal length and object distance.

Finally, calculate the scale factor of the image using values of object distance and image distance. Fundamentals

Focal length is defined as the distance between the center of a lens and the focal point of the lens.

Object distance is defined as the distance of the object from the center of a lens.

For thin lenses, the object distance is denoted by the symbol ppp .

Image distance is defined as the distance of the image from the center of a lens.

For thin lenses, the image distance is denoted by the symbol q{\rm{q}}q .

Magnification is defined as the ratio of image distance to the object distance.

Magnification=−ImagedistanceObjectdistance{\rm{Magnification = }}\frac{{{\rm{ – }}\,{\rm{Image}}\,{\rm{distance}}}}{{{\rm{Object}}\,{\rm{distance}}}}Magnification=Objectdistance−Imagedistance​

Lens formula is expressed as,

1f=1p+1q\frac{1}{f} = \frac{1}{p} + \frac{1}{q}f1​=p1​+q1​

Here, the focal length of the thin lens is fff , the object distance is ppp and image distance is qqq .

In the below figure describes the image created by thin lens,

FigureL Image creation by thin lens
Object
Image
Converging
lens

The scale factor can be calculated by using below expression,

ScaleFactor=∣Imagedistance∣∣Objectdistance∣{\rm{Scale Factor = }}\frac{{|\,{\rm{Image}}\,\,{\rm{distance|}}}}{{{\rm{|Object}}\,{\rm{distance|}}}}ScaleFactor=∣Objectdistance∣∣Imagedistance∣​ Show more First Step | All Steps | Answer Only

Step-by-step

Step 1 of 4

(a)

Express the magnification of thin lens,

Magnification=−ImagedistanceObjectdistance{\rm{Magnification = }}\frac{{{\rm{ – }}\,{\rm{Image}}\,{\rm{distance}}}}{{{\rm{Object}}\,{\rm{distance}}}}Magnification=Objectdistance−Imagedistance​

Substitute qqq for Image distance and ppp for object distance

M=−qpM{\rm{ = }}\frac{{ – q}}{p}M=p−q​ Part a

The magnification equation is qp−1{\bf{q}}{{\bf{p}}^{{\bf{ – 1}}}}qp−1
Explanation | Common mistakes | Hint for next step

Variables of the image distance and object distance are used in the expression of magnification to get the required equation.

Do not use a formula M=pq{\rm{M = }}\frac{p}{q}M=qp​ to express the magnification equation. It is a mistake because the correct formula is M=qp{\rm{M = }}\frac{q}{{\rm{p}}}M=pq​ .

Use distance between eyepiece and focal length of objective lens to find relation between objective lens and eye piece.

Step 2 of 4

(b)

Eye piece is the lens close to the eye.

The objective lens collects lights and brings it to focus on creating an image. The eyepiece is placed near the focal point of the objective lens.

As a result of which eyepiece takes the objective’s real image and creates a magnified virtual image. Part b

The eyepiece takes the objective’s real image and creates a magnified virtual image.
Explanation | Common mistakes | Hint for next step

To explain the working of eye piece, its position with the objective lens is used. Since the eyepiece is near the focus of objective, it takes the light collected by the objective at its focus.

Use the lens formula to calculate the image distance using given object distance and focal length of the lens.

Use lens formula to calculate image distance.

Step 3 of 4

(c)

Express the lens formula for object distance and image distance.

1f=1p+1q\frac{1}{f} = \frac{1}{p} + \frac{1}{q}f1​=p1​+q1​

Here, the focal length of the thin lens is fff , the object distance is ppp and image distance is qqq .

Substitute 41mm41\,{\rm{mm}}41mm for ppp , 162mm162\,{\rm{mm}}162mm for qqq and solve for q.

1f=1p+1q\frac{1}{f} = \frac{1}{p} + \frac{1}{q}f1​=p1​+q1​

1162=141+1q\frac{1}{{162}} = \frac{1}{{41}} + \frac{1}{q}1621​=411​+q1​

q=−54.86mmq = – 54.86\,{\rm{mm}}q=−54.86mm

Negative sign of the image distance indicates image is virtual and located on objects side of the lens.Part c

Image distance is −54.86mm{\bf{ – }}\,{\bf{54}}{\bf{.86}}\,{\bf{mm}}−54.86mm .
Explanation | Common mistakes | Hint for next step

Lens formula is used to calculate image distance. Values of the object distance and focal length are used in the expression to get image distance.

Do not use 1f=1p2+1q2\frac{1}{f} = \frac{1}{{{p^2}}} + \frac{1}{{{q^2}}}f1​=p21​+q21​ to calculate the image distance. It is incorrect because the correct formula is 1f=1p+1q\frac{1}{f} = \frac{1}{p} + \frac{1}{q}f1​=p1​+q1​ .

Use lens formula to calculate scale factor.

Step 4 of 4

(d)

Express the scale factor for the thin lens using object distance and image distance

scalefactor=∣q∣∣p∣{\rm{scale}}\,{\rm{factor}} = \frac{{|q|}}{{|p|}}scalefactor=∣p∣∣q∣​

Substitute 41mm41\,{\rm{mm}}41mm for ppp and −54.86mm – 54.86\,{\rm{mm}}−54.86mm for qqq

scalefactor=∣54.86∣∣41∣scalefactor=1.34 = 1.34\\\end{array}scalefactor 1.34​ Part d

The scale factor is 1.34 .
Explanation | Common mistakes

The expression of the scale factor is used to determine its value. The values of object distance and focal length are used in the scale factor to calculate its value.

Do not use a formula scalefactor=∣p∣∣q∣{\rm{scale}}\,{\rm{factor}} = \frac{{|p|}}{{|q|}}scalefactor=∣q∣∣p∣​ to calculate the scale factor. It is a mistake because the correct formula is scalefactor=∣q∣∣p∣{\rm{scale}}\,{\rm{factor}} = \frac{{|q|}}{{|p|}}scalefactor=∣p∣∣q∣​ .

Answer

Part a

The magnification equation is qp−1

Part b

The eyepiece takes the objective’s real image and creates a magnified virtual image.

Part c

Image distance is −54.86mm .

Part d

The scale factor is 1.34 .


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