Question

an object is placed at a distance of 20cm from a concave lens of focal length 15 cm. find position,size,and nature of an image.​

Answer 1

Answer:

Ray diagrams can be used to determine the image location, size, orientation and type of image formed of

objects when placed at a given location in front of a concave mirror. The use of these diagrams was demonstrated . Ray diagrams provide useful information about object-image relationships, yet fail to provide the information in a quantitative form. While a ray diagram may help one determine the approximate location and size of the image, it will not provide numerical information about image distance and object size.

To obtain this type of numerical information, it is necessary to use the

Mirror Equation

and the

Magnification Equation

. The mirror equation expresses the quantitative relationship between the object distance (do), the image distance (di), and the focal length (f). The equation is stated as follows:

The magnification equation relates the ratio of the image distance and object-distance to the ratio of the image height (hi) and object height (ho). The magnification equation is stated as follows:

These two equations can be combined to yield information about the image distance and image height if the object distance, object height, and focal length are known.

ref.

In the present problem, the object is placed at a position which is between f and 2f so the image will be formed between infinity and 2f.

logic is had the object been at f …the image will be at infinity and if it is at 2f the image will come to 2f

using the mirror relation

1/v + 1/u = 1/f where u, v, f are object distance, image distance, and focal length respectively.

u= 20 cm f=15 cm (the sign convention is a coordinate convention with the mirror at origin and object on the positive x-axis)

so 1/v = 1/f - 1/u , = 1/15 - 1/20

= 5/(15x20)= 1/60 therefore v= 60 cm

so the image will be formed at 60 cm

with magnification m= v/u = 60/20 = 3

the image will be 3 times larger and real

Answer 2

Explanation:

An object is placed at a distance of 20cm from a concave mirror with a focal length of 15cm. What is the position and nature of the image?

Ray diagrams can be used to determine the image location, size, orientation and type of image formed of

Objects when placed at a given location in front of a concave mirror. The use of these diagrams was demonstrated .

Ray diagrams provide useful information about object-image relationships, yet fail to provide the information in a quantitative form.

While a ray diagram may help one determine the approximate location and size of the image, it will not provide numerical information about image distance and object size.

To obtain this type of numerical information, it is necessary.

We can see Object distance (u) is 20cm.

Focal length (f)= 15 cm.

By using sign convention , in concave mirror,

u and f both -(ve).

There is a formula 1/u+1/v=1/f

Buy using this formula we can find the v.

v= 1/f - 1/u

v= -1/15 - 1/20

v= -60cm

So we can now say that the position of the image will be 60 cm from the mirror.

To identify the nature of the image, we have to use the formula of magnification (m)

m= hi/ho=-v/u

If it is +(ve) then image will be virtual and erect and vice versa.

m= -(-60)/-20

m= -3

So nature of the image is Real and Inverted.

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