Question

(a) An object 3 cm high is placed 24 cm away from a convex lens of focal length 8 cm. Find by calculations, the position, height and nature of the image.
(b) If the object is moved to a point only 3 cm away from the lens, what is the new position, height and nature of the image?
(c) Which of the above two cases illustrates the working of a magnifying glass?

Answer 1

Explanation:

(a) Step 1:

Given data in the question  

Object distance (u) = -24  

Focal length (f) = +8  

Object height (h) = 3  

Formula for the lens is given by:  

$\frac{1}{f} =\frac{1}{v} -\frac{1}{u}$

$\frac{1}{8} =\frac{1}{v} -\frac{1}{-24}$

$\frac{1}{8} =\frac{1}{v} +\frac{1}{24}$

$\frac{1}{8} -\frac{1}{24} =\frac{1}{v}$

$\frac{3-1}{24} =\frac{1}{v}$

$\frac{2}{24} =\frac{1}{v}$

v=12 cm

The picture on the right side of the convex lens will be produced at a distance of 12 cm.

Step 2:

Magnification  

$m=\frac{v}{u}$

$m=\frac{12}{-24}$

$m= -\frac{1}{2}$

So, the picture diminishes.

The negative magnification value means the picture will be true and inverted.

$m=h_i/h_0$

$-\frac{1}{2} =\frac{h_i}{3}$

$h_i = -\frac{3}{2}$    

$h_i =-1.5 cm$

The picture will be 1.5 cm high. Here, negative sign indicates the picture is going downwards.

(b) Step 1:  

Given Object distance (u) = -3

$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$

On substituting the values, we get

$\frac{1}{8} =\frac{1}{v} -\frac{1}{-3}$

$\frac{1}{8} = \frac{1}{v} + \frac{1}{3}$

$\frac{1}{8} -\frac{1}{3} = \frac{1}{v}$

$v= -\frac{24}{5}$

v= -4.8 cm

The image is to be at a distance of 4.8 cm before the lens

$m=\frac{v}{u}$                  

m=$\frac{-4.8}{-3}$

m= 1.6

Step 2:

Positive magnification value indicates the image is both virtual and upright.

$m=\frac{h_i}{h_0 }$

$1.6=\frac{ h_i}{3}$

$h_i =4.8 cm$

Positive image sign indicates the image is formed above the main axis.    

(c) Case (b) shows the magnifying lens working as the object is between the focus center and the optical centre.

You can get all the answers of Chapter 5 in the link below:    

https://brainly.in/question/14963222

   

Few questions related to this chapter:    

(a) Find the nature, position and magnification of the images formed by a c.....

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A convex lens produces a magnification of + 5. The object is placed

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Answer 2

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