Divergent Glass lens question

[soccerpie]

In the book it asks this question:

A divergent glass lens has a focal length of 80 centimeters. An object is held in front of it at a distance of 20 centimeters. Determine whether the image is real, virtual, upright, or inverted?

Im using the thin lens equation: 1/f= 1/o +1/i

in the answer it rights 1/-80=1/20+1/i but im confused why this is? i know 80 is negative because the focal length is located in front of the divergent lens, but why is the object distance positive when in the question it says that the object is also held in front of the divergent lens, so shouldnt it be negative? that would be a great help!!!
thanks

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[homestar]

The sign conventions look correct as far as I can see. As you rightly state, the focal length of a diverging lens (concave) is negative (behind the lens). An object held in front of the lens would naturally have a positive object distance (opposite to that of the negative focal length.

I come out with di = -16, which means that the image would be virtual. I calculate the magnification to 0.8, which means that the image is smaller (less than the absolute value of one) than the object, and that it is upright (positive).

I confirmed these numbers with a Java applet.

 

[HaraiGoshi]

Objects in front of a mirror or a lens will always be positive, and in any single lens or mirror system they have to be positive (or the system wouldn't work).

I also got -16 using the thin lens equation.

 

[JFK90787]

On top of knowing all your optics equations, I would recommend playing around with this website for like half an hour. It helped me to answer those questions intuitively without needing the equations most of the time

http://www.phys.hawaii.edu/~teb/java/ntnujava/Lens/lens_e.html

 

[IntelInside]

In the book it asks this question:

A divergent glass lens has a focal length of 80 centimeters. An object is held in front of it at a distance of 20 centimeters. Determine whether the image is real, virtual, upright, or inverted?

Im using the thin lens equation: 1/f= 1/o +1/i

in the answer it rights 1/-80=1/20+1/i but im confused why this is? i know 80 is negative because the focal length is located in front of the divergent lens, but why is the object distance positive when in the question it says that the object is also held in front of the divergent lens, so shouldnt it be negative? that would be a great help!!!
thanks

Here is the summary I like to use:

Summary of the mirror’s and lenses

For a flat mirror:
- The image is unmagnified virtual and upright!!
- The image is as far behind the mirror as the object is in front

For a concave mirror:
- it makes a positive, real, inverted image that is smaller

- ** Exception **: if the object is moved within the focal distance it will make a negative virtual upright image on the side of the mirror opposite the object and is larger.

- Focal distance and center of curvature are positive!!

For a convex mirror:
- it makes a negative, virtual, upright image and image is smaller
- Focal distance and center of curvature are negative!!

For converging (convex) lens:
- it makes a positive, real, inverted image that is smaller than the object

- ** Exception **: if the object is moved within the focal distance it will make a negative virtual upright image on the side of the lens with the object. That is larger than the object

- f distance is always positive

For a diverging (concave) lens:
- It makes a negative, virtual, upright image and image is always smaller!!

- Only makes images within 1 focal length of itself (in a one lens system)!!!

- f distance is always negative

 

[BerkReviewTeach]

Here is the summary I like to use:

Summary of the mirror’s and lenses

For a flat mirror:
- The image is unmagnified virtual and upright!!
- The image is as far behind the mirror as the object is in front

For a concave mirror:
- it makes a positive, real, inverted image that is smaller

- ** Exception **: if the object is moved within the focal distance it will make a negative virtual upright image on the side of the mirror opposite the object and is larger.

- Focal distance and center of curvature are positive!!

For a convex mirror:
- it makes a negative, virtual, upright image and image is smaller
- Focal distance and center of curvature are negative!!

For converging (convex) lens:
- it makes a positive, real, inverted image that is smaller than the object

- ** Exception **: if the object is moved within the focal distance it will make a negative virtual upright image on the side of the lens with the object. That is larger than the object

- f distance is always positive

For a diverging (concave) lens:
- It makes a negative, virtual, upright image and image is always smaller!!

- Only makes images within 1 focal length of itself (in a one lens system)!!!

- f distance is always negative

Pretty good summary, but you may want to reconsider your list for a concave mirror and convering lens when the object lies between the R and f, because the image forms beyond the R, making it larger. Other than that, your list is solid and emphasizes the key things people seem to forget.

 

[IntelInside]

Pretty good summary, but you may want to reconsider your list for a concave mirror and convering lens when the object lies between the R and f, because the image forms beyond the R, making it larger. Other than that, your list is solid and emphasizes the key things people seem to forget.

that is what the exceptions are for....