Two lenses having focal lengths f1=+9.0 cm and f2=-18.0 cm are placed 3.0 cm apart. If an obj

step 1 So in this question we are given two lenses like this. The distance between the lenses is given

Two lenses having focal lengths f1=+9.0 cm and f2=-18.0 cm...

Key Concepts

Graphical Ray Diagrams

Graphical ray diagrams are sketches that trace selected rays from the object through the lenses to construct the image location and size visually. They serve as an effective check on analytical calculations, confirming the results of the lens equations and magnification factors.

Sequential Image Formation in Multiple Lens Systems

In systems with multiple lenses, the image produced by the first lens serves as the object for the second lens. It is important to adjust the object distance for subsequent lenses by accounting for the separation between the lenses, ensuring accurate determination of the final image properties.

Magnification

Magnification relates the height of the image to the height of the object and is given by the ratio of the image distance to the object distance (with a sign to indicate image inversion if applicable). It provides insight into the size change of the object as it is imaged by the lens system.

Thin Lens Equation

The thin lens equation (1/f = 1/do + 1/di) is fundamental for determining the relationship between object distance, image distance, and focal length of a thin lens. It allows one to calculate the image’s position when the object’s position and the lens’s focal length are known.

Sign Conventions in Optics

Sign conventions in optics are crucial for correctly applying formulas in image formation. They determine the positive or negative values for object distances, image distances, and focal lengths based on their positions relative to the lens, which in turn indicates whether images are real or virtual.

Transcript

00:01 So in this question we are given two lenses like this.

00:09 The distance between the lenses is given which is 3 cm, focal length 9 cm, focal length here is minus 18 cm and on the principal axis there is an object of height 2 .5 centimeter the distance from the first lens is also given which is 20 centimeter we need to find the location of the final image the size of the image all right so let's see how to calculate that so we are applying lens maker formula for the first lens one by v minus 1 by u is equal to 1 by f 1 by v i'm calling it 1 minus 1 by u you would be minus 20 you can see that this is minus 20 because lying on the negative x -axis so is equal to 1 by focal length so we know our focal length is 9 in this case so definitely from here we can get the value of v1 the value of the v1 it is coming out be 16 .36 which means the first lens will try to make an image at a distance of 16 .36 and this image will serve as an object for this lens.

01:56 So from here if you see this distance, this would be 16 .36 minus 16 .36 minus 3 cm which is 13 .36.

02:11 So now this will serve as an object.

02:14 So object distance for the second lens is going to be 13 .36.

02:19 Again we are applying lens maker formula.

02:23 Lens formula.

02:25 So 1 by v minus 1 by u is equal to 1 by f.

02:31 1 by b we are calling b2 minus 1 by u which is 13 .36.

02:38 The object distance from the second lens right so is equal to one upon focal length is given to us which is minus 18 so now we can get the value we do again from here by doing the calculations and this value is coming out to be 51 .51 1 .83 centimeter which implies the final image the final image final image is at a distance of 51 .8 3 cm from where from the second lens so this is the position of the final image now we need to find the size also now how we can find the size.

03:37 We can find the magnification in the first lens and then magnification in the second lens and then we can multiply the magnifications through get the net magnification.

03:46 So magnification by the first lens is equal to image distance 16 .36 divided by object distance.

04:01 Okay.

04:02 For the first lens it is 20 so it is definitely minus 20...

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