# Heat production of magnifying glass

Why Magnifying glass(convex lens) produces heat when placed in front of sun?

• It doesn't. Do you know what a convex lens does with light? – Carl Witthoft Mar 11 '14 at 15:53
• @CarlWitthoft Then why do a paper gets burnt when placed under it? – Praveen Kadambari Mar 11 '14 at 15:57

When you focus light from the Sun you are actually creating an image of the Sun. If the focal length of the lens is $f$ the radius of the image is given by:

$$r = \frac{r_s}{d_s} f$$

where $d_s$ is the distance to the Sun and $r_s$ is the radius of the Sun. The fraction $r_s/d_s \approx 10^{-3}$, so if you choose a lens with a focal length of 10cm the radius of the image is about 0.1mm (assuming the lens is perfect).

The intensity of sunlight is around 1kW per square metre - the exact value depends on latitude, season, time of day, cloud cover, etc, etc so let's just take 1kW/m$^2$ as a representative figure. All the light falling on your lens is being concentrated into the 0.1mm radius image of the Sun, so if the radius of your lens is $r_l$ the power per unit area in the image is:

$$I = \left(\frac{r_l}{0.1 mm} \right)^2 1kW/m^2$$

So if the lens radius is 5 cm, which seems a fairly standard size for a lens, then the power per unit area in the focussed image of the Sun is about 250MW/m$^2$ or 250,000 times the intensity of Sunlight on the Earth. That's why it's hot!

Of course the total power isn't very great, because even though the focussed light is very intense the area of the 0.1 mm image is only about $3 \times 10^{-8}$ square metres. The total power is just the area over which light is being collected (the area of your lens) times 1 kW. A bigger lens will capture more sunlight and focus more power.

It is the sun that produces the energy that falls on the convex lens in the form of light (and a bit more than just light in the visible part of the spectrum). The lens concentrates all this light in a small spot. A good fraction of the energy is converted to heat if the material at the focal point is suitable.

• +1. The sun is incredibly inefficient, when you think about it. Why don't we invest in a compact fluorescent star… – Blackbody Blacklight Mar 11 '14 at 17:02

The lens focuses light due to refraction. Absorbance of light by a surface creates heat. More intense light due to focusing creates more heat per unit area at the focal region.