Final answer:
The change in focal length of a convex lens when submerged in water can be calculated using the lensmaker's equation by substituting the refractive index of the medium with water's refractive index. Once the lens power in water is calculated, the inverse gives the new focal length, which can be compared with the original focal length to find the change.
Step-by-step explanation:
The question is asking about the change in the focal length of a convex lens when it is submerged in water compared to its focal length in air. The lens has a refractive index of 1.5 and an initial focal length of 18 cm in air. The focal length of a lens changes according to the medium it is in due to the change in refractive index.
The lensmaker's equation can be used to find the focal length of a lens, which is given by:
1/f = (n_l - n_m) × (1/R_1 - 1/R_2)
where f is the focal length of the lens, n_l is the refractive index of the lens material, n_m is the refractive index of the medium the lens is in, and R_1 and R_2 are the radii of curvature of the lens surfaces.
When the lens is immersed in water, only the refractive index of the surrounding medium changes (n_water = 4/3). Thus the new focal length (f') can be calculated via the lensmaker's equation by using the refractive index of water instead of air.
First, find the lens power in air (P_air). The power of a lens is the inverse of the focal length (P = 1/f). So,
P_air = 1/18 cm
Next, calculate the lens power in water (P_water) using the refractive indices:
P_water = (n_l - n_water) × P_air / (n_l - n_air).
Then, the new focal length in water (f') is just the inverse of P_water:
f' = 1 / P_water
By calculating f', we can determine the change in focal length by subtracting the initial focal length in air from the new focal length in water. Remember that due to the change in medium, the lens may become less powerful and thus have a longer focal length, resulting in a positive change in cm.