Find the change in the focal length of the eye
when an object originally at 4 m is brought
to 26 cm from the eye. [The retina is 2.5 cm
from the lens of the eye.]
Answer in units of mm.
Need Help!!!!!!
To find the change in the focal length of the eye, we can use the lens formula:
1/f = 1/v - 1/u,
where f is the focal length of the eye, v is the image distance, and u is the object distance.
Given:
The object distance, u = 4 m = 400 cm.
The image distance, v = 26 cm.
The distance from the lens to the retina, which is the distance from the eye's lens to the final image position, is 2.5 cm.
Now we need to calculate the initial focal length, f_initial, using the lens formula. We will take the initial object distance as u_initial = 400 cm and the corresponding image distance as v_initial.
1/f_initial = 1/v_initial - 1/u_initial
Solving for f_initial:
1/f_initial = 1/v_initial - 1/u_initial
1/f_initial = 1/v_initial - 1/400
Now, calculate f_initial.
To find the final focal length, f_final, we need to consider the new object and image distances after moving the object to 26 cm from the eye.
The new object distance, u_final = v_initial + 2.5 cm.
The new image distance, v_final = 2.5 cm (since the retina is 2.5 cm from the lens).
Substituting these values into the lens formula:
1/f_final = 1/v_final - 1/u_final
Now, calculate f_final.
Finally, the change in focal length, Δf, can be obtained by subtracting f_initial from f_final:
Δf = f_final - f_initial.
Calculating all these values will give us the change in the focal length of the eye. Let me calculate it for you.