Question

A student focuses the image of a candle flame on a white screen using a convex lens. He noted down the position of the candle screen and the lens as shown below
Position of candle = 12.0 cm
Position of convex lens = 50.0 cm
Position of the screen = 88.0 cm
(i) What is the focal length of the convex lens?
(ii) Where will the image be formed if he shifts the candle towards the lens at a position of 31.0 cm?
(iii) What will be the nature of the image formed if he further shifts the candle towards the lens?
(iv) Draw a ray diagram to show the formation of the image in case (iii) as said above.

Answer 1

Step 1: Given that:

Position of candle = $\text{12.0cm}$

Position of convex lens = $\text{50.0cm}$

Position of the screen = $\text{88.0cm}$

Step 2: Calculation of object distance and image distance:

Object distance(u) = Distance between the lens and the object

u = Position of the convex lens - Position of candle

u = $-(50cm-12cm)$

u = $-38cm$

Image distance = Distance between the lens and the image

v = Position of the screen at which the image is formed - Position of the convex lens

v = $+(88cm-50cm)$

v = $+38cm$

Step 3: i) Calculation of the focal length of the convex lens:

Object distance(u) = $-38cm$

Image distance(v) = $+38cm$

We can see that the object distance(u) = Image distance(v)

It means,

The object is placed at the centre of the curvature of the convex lens.

Thus, the radius of curvature($R$) = $+38cm$

Focal length(f) of a lens = $\frac{Radiusofcurvature\left(R\right)}{2}$

Therefore;

$f=\frac{38cm}{2}$

$f=+19cm$

Step 4: ii) The position of the image when the candle is shifted to 31cm:

Object distance = Distance between the lens and the object

= Position of the convex lens - Position of the candle

= $-(50cm-31cm)$

u = $-19cm$

Since Object distance(u) = Focal length of the lens(f)

Therefore, the image of the candle will be formed at inifinity.

Step 5: iii) Determination of the nature of the image when the candle is shifted further towards the lens:

1. When the candle is shifted towards the lens, it means the candle is placed somewhere between the optical centre and the focus of the convex lens.
2. Thus, the image of the candle will be formed on the same side of the object.
3. The image will be virtual and erect.
4. The image will be magnified that is the size of the image is larger than the object that is the candle.

Step 6: iv) Ray diagram to show the formation of the image for the case when the candle is placed between the optical centre and focus of the convex lens: