Answer:
The focal length of the lens is 26 cm
Explanation:
Focal length (f) of the lens is the distance between the lens and the image. It is also the distance between the lens axis and principal focus.
Applying lens formula;
[tex]\frac{1}{f} = \frac{1}{di} +\frac{1}{do}[/tex]
where;
f is the focal length
di is the image distance
do is the object distance
The object distance in this question is the distance of the sun from the lens, this distance is too large, and its inverse is infinitesimal.
The equation above will reduce to;
[tex]\frac{1}{f} = \frac{1}{di}[/tex]
given;
di = 26 cm
[tex]\frac{1}{f} = \frac{1}{26}\\\\f = 26cm[/tex]
Therefore, the focal length of the lens is 26 cm
26cm
For a convex lens, its focal point or focus is the point where parallel rays are made to converge on it and the distance between the center of the lens and this focal point is called the focal length.
The relationship between the focal length (f) of a convex lens, the distance of the object ([tex]d_{O}[/tex]) under view by the lens, and distance of the image ([tex]d_{I}[/tex]) of the object formed by the lens, from the center of the lens is given as follows;
[tex]\frac{1}{f}[/tex] = [tex]\frac{1}{d_{O} }[/tex] + [tex]\frac{1}{d_{I} }[/tex] -----------------------(i)
Note from the question;
(i) The object under view is the sun and the distance, [tex]d_{O}[/tex], of the object (sun) from the lens is so large that it can be approximately equal to infinity (∞). This implies that, approximately;
=> [tex]d_{O}[/tex] = ∞
=> [tex]\frac{1}{d_{O} }[/tex] = 0
(ii) The image of the sun formed on the paper is 26cm below/from the lens. This implies that [tex]d_{I}[/tex] = 26cm
Now substitute [tex]\frac{1}{d_{O} }[/tex] = 0 and [tex]d_{I}[/tex] = 26cm into equation (i) as follows;
=> [tex]\frac{1}{f}[/tex] = 0 + [tex]\frac{1}{26}[/tex]
=> [tex]\frac{1}{f}[/tex] = [tex]\frac{1}{26}[/tex]
Cross mulitiply and solve for f;
f = 26cm
Therefore, the focal length of the lens is 26cm
