In Lens I1 ,
P=+10D
So P=1/f (in metre )
f =0.1 metre and its convex lens since focal length is positive

In Lens I2,
P=+5D
f=1/P
f=1/5 =0.2 metre and its again convex lens .

In Len I3,
P=-10D
f=1/D
f=1/-10
f=-0.1 metre and its concave lens since focal length is negative .
(Sign Convetion is important in these questions and it's very easy :) )

Nature and Focal Length of Lenses

• Lens L1 with power 10D is a convex lens.


• Focal length of L1 can be calculated using the formula 1/f = (n-1)(1/R1 - 1/R2), where R1 and R2 are radii of curvature of the two surfaces of the lens. For simplicity, assuming both surfaces are of equal curvature, we can use R as the radius of curvature. Here, n is the refractive index of the lens material, which is typically around 1.5 for glass lenses. Plugging in the values, we get f = 10 cm. Hence, the focal length of L1 is 10 cm.


• Lens L2 with power 5D is also a convex lens.


• Using the same formula as above, we can calculate the focal length of L2 as 20 cm.


• Lens L3 with power -10D is a concave lens.


• The focal length of a concave lens is negative. Using the same formula as above, we can calculate the focal length of L3 as -10 cm.

Explanation

The power of a lens is defined as the inverse of its focal length, in meters. Therefore, a lens with a power of 10D has a focal length of 0.1 m or 10 cm. This lens is a convex lens, which means it converges light rays to a point. Similarly, a lens with a power of 5D has a focal length of 0.2 m or 20 cm. This lens is also a convex lens. On the other hand, a lens with a power of -10D has a focal length of -0.1 m or -10 cm. This lens is a concave lens, which means it diverges light rays.

The formula for calculating the focal length of a lens is based on the idea that light rays passing through a lens converge or diverge depending on the curvature of the lens surfaces. A convex lens has two surfaces that bulge outwards, while a concave lens has two surfaces that curve inwards. The radius of curvature of these surfaces determines how much the lens bends the light rays passing through it. By calculating the radii of curvature and the refractive index of the lens material, we can determine the focal length of the lens.

In summary, knowing the power of a lens allows us to determine its focal length and its nature as either a convex or concave lens. This information is important in understanding how light interacts with lenses and how they can be used to form images.