Question

the nature of the graph between 1 / u and 1 / v for a convex lens where u is the distance of the object and v is that of image is​

Answer 1

Answer:

The nature of the graph between 1 / u and 1 / v for a convex lens where u is the distance of the object and v is that of image is​ hyperbola.

Explanation:

According to question we need to find out the nature of the graph between 1 / u and 1 / v for a convex lens where u is the distance of the object and v is the distance of the image .

Let f = focal length of the convex lens.

u = distance of the object.

v = distance of the image.

For convex lens

$\frac{1}{f} = \frac{1}{v} - \frac{1}{u} \\\\or , \frac{1}{f} = \frac{u-v}{uv}\\ \\or , f = \frac{uv}{u-v}$

So , the nature of the graph between 1 / u and 1 / v for a convex lens where u is the distance of the object and v is that of image is​ hyperbola.

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Answer 2

Answer: The nature of the graph between 1/u and 1/v for a convex lens is a straight line with positive intercept on 1/v axis and negative intercept on 1/u axis.

Explanation:

Lens formula :  $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$

v ⇒ Image distance

u ⇒ Object distance

f ⇒ Focal length of lens

Focal length of convex lens is positive.

Let the focal length of lens be 1/c ( c > 0 )

If we represent  1/v  on y-axis and  1/u  on x-axis , Lens formula will be rewritten as :  y - x  = c

It represents a straight line.

Hence,

The graph between 1/u and 1/v for a convex lens will be a straight line.

Line will have positive intercept on 1/v axis and negative intercept on 1/u axis.

The value of intercept will change depending on the value of focal length of the lens.

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