Question

An object of size 10cm is kept at a distance of 10cm from a convex lens. If the focal length of the lens is 5cm, the size of the image is

Answer 1

Answer on Question 59113, Physics, Optics

Question:

An object of size $10\, \text{cm}$ is kept at a distance of $10\, \text{cm}$ from a convex lens. If the focal length of the lens is $5\, \text{cm}$, the size of the image is ___?

Solution:

Let’s first find the distance from the convex lens to the image from the lens equation:

$$\frac{1}{d_o} + \frac{1}{d_i} = \frac{1}{f},$$

here, $d_o$ is the distance from the object to the convex lens, $d_i$ is the distance from the convex lens to the image and $f$ is the focal length.

So, we get:

$$\frac{1}{10\, \text{cm}} + \frac{1}{d_i} = \frac{1}{5\, \text{cm}},$$ $$\frac{1}{d_i} = \frac{1}{5\, \text{cm}} - \frac{1}{10\, \text{cm}} = \frac{1}{10}\, \text{cm},$$ $$d_i = 10\, \text{cm}.$$

As we can see, the distance from the lens to the image is positive, so the image is real.

Then, we can calculate the magnification of the lens from the formula:

$$M = \frac{h_i}{h_0} = \frac{-d_i}{d_o},$$

here, $h_i$ is the size of the image, $h_0$ is the size of the object, $d_o$ is the distance from the object to the convex lens, $d_i$ is the distance from the convex lens to the image.

Thus, we get:

$$M = \frac{-d_i}{d_o} = \frac{-10\, \text{cm}}{10\, \text{cm}} = -1.$$

As we know, the magnification, we can find the size of the image:

$$h _ {i} = M \cdot h _ {0} = (- 1) \cdot 10 \text{ cm} = - 10 \text{ cm}.$$

The sign minus indicates that the image is inverted. As we can see the image is the same size as the object.

Let's draw the ray tracing diagram:

The object is located at a distance of two focal point $(2F)$ from the lens (here, 1 cell is equal to 1 centimeter). According to the theory, we obtain a real, inverted image, that is the same size as the object and located at a distance of two focal point on the other side of the convex lens.

Answer:

$$h _ {i} = - 10 \text{ cm}.$$

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