Why electric field has a major role in vision? Although the electromagnetic wave is made op of both electric and magnetic fields the electric field contributes much in vision and is thus, called the light vector. But, why is it that the electric field has a major role?  
 A: The vision of our eye is due to the force experienced by the moving charge 
on our retina. The moving charge experiences force both due to electric & 
magnetic fields. 
Force due to electric field: qE
Force due to magnetic field: qVB
Ratio of these two forces=E/VB
                   =C/V

                   =10^8/V

Therefore, moving particle oscillates primarily due to the electric field and hence electric field has a major role in the process of vision.
A: In the electromagnetic radiation, it is the Electric field, $\vec{E}(r,t)$ which has higher magnitude than the magnetic field $\vec{B}(r,t)$. The formal expression for these fields can be derived from the Maxwell's equation:
$$
\vec{E}(\vec{r},t) = -\vec{\nabla}{\phi}(\vec{r},t) - \frac{\partial \vec{A}(\vec{r},t)}{\partial t} \tag{1}
$$
$$
\vec{B}(\vec{r},t) = \vec{\nabla} \times \vec{A}(\vec{r},t) \tag{2}
$$
Here we assume that this EM radiation is in vacuum so there are no external electric and magnetic fields. We choose the Coulomb gauge:
$$
\vec{\nabla}.\vec{A}(\vec{r},t) = 0 \tag{3}
$$
Using the maxwell's equation we can show that $\vec{A}(\vec{r},t)$ satisfies the wave equation:
$$
\vec{\nabla}^2 \vec{A}(\vec{r},t) - \frac{1}{c^2} \frac{\partial ^2\vec{A}(\vec{r},t)}{\partial^2t} = 0 \tag{4}
$$
This equation gives the following solution:
$$
\vec{A} = 2\vec{A}_{0}(\omega)cos(\vec{k}.\vec{r}-\omega t + \phi) \tag{5}
$$
Here $\vec{A}_{0}(\omega)$ determines the intensity and and polarisation direction of the radiation. If $\vec{k}$ is the direction of propagation of the radiation then:
$$
\vec{k}.\vec{A}_{0}(\omega) = 0 \tag{6}$$
Since the radiation is transverse in nature. The electric and magnetic fields associated with this vector potential can be found using (1) and (2) to be:
$$
\vec{E} = -2\omega A_{0}(\omega)sin(\vec{k}.\vec{r} - \omega t + \phi)\hat{\epsilon} \tag{7}
$$
$$
\vec{B} = -2A_{0}(\omega)sin(\vec{k}.\vec{r} - \omega t + \phi)\vec{k}\times \hat{\epsilon} \tag{8}
$$
Since $\omega$ for say visible light is of very high order, we can say that most effects associated with electromagnetic radiation are due to this electric field.
A: What do we Know about Vision ?  - The Electric Field Explanation of Refraction and its Role.
Introduction
Note to readers: This is written in an easy-to-understand manner and is consistent with the known explanations given by prominent physicists without going into the greatest level of detail possible.
Light travels close to 300,000,000 metres/second which means that it reaches us from the sun in 500 seconds.
When light encounters solid or liquid materials most times it reflects off the surface but in other cases such as water, glass and any item we call transparent it enters the material and most of it goes out the other side. 
Light oscillates and may be viewed as somewhat similar to a rapidly moving helical spring. The spring has a regular spacing between its turns and for light the corresponding property is its wavelength.  The material squeezes the light in its direction of travel - reducing its wave-length in the same way one may push in on each end of a helical spring causing its spiral to compress. This is called refraction.
Electric Field Interactions
It is the electric field of the material which compresses the wavelength of the light to become compressed. We can imagine the incoming light causing a small dent in the surface of the material by making a dent in the electric field of the material (at the material's boundary) as it pushes its way through the surface. This dent will have a depth and a width. (The depth will depend on the type of material and on the number of photons passing into it a much the same location. Its width will be a function of the amplitude of the photon's electric field.) The photon is moving forwards and its electric field oscillates in and out to the side. The overall effect is an electric field which (from the material's point of view is pointing into it a sharp angle and its field pushes the direction of the field into a less acute angle. And, this sets in motion a wave within the material away from the photon - the atoms in the region vibrate and their vibration moves outward.
Vision
In our personal optical systems the wave is piped along nerves called optic nerves which take the signal from the light receptors in the retina of our eyes to the visual cortex at the back of our heads where the visualization process takes place.  The signals can be detected as tiny voltage variations detectable on the scalp.  Normally other electrical noise would swamp such signals. However, when the eye sees a repeated pattern for a minute or so the electrical pulses from its changing can be accumulated with the signal emerging as the background noise averages to around zero,  This is the basis of electro-diagnostic tests to determine whether optic nerves are carrying a signal or not.
Changing the Speed of Light
In the case of water its electric field causes the wavelength of photons passing into it to close up to 2/3 their normal wavelength and the light takes 3/2 times the time to travel the same distance as normal when it is passing through the water. The time factor change is called the refractive index and as you may have deduced is always greater than 1.
Thus, our personal optical systems act as signal transducers changing the energy of a photon into an electrical signal carried by our optic nerves for further processing.
Our Eyes
In fact our personal optical systems (eyes) have 3 stages
The light passes through the lens of the eye which is a convex shape varying in thickness from thin to fat to thin and the other feature of refraction (change of direction on passing through a boundary between materials of different types) causes the light to focus as an image on the retina at the back of each eye. 
The middle stage is passing through the water between the lens and the retina and there is not much change here. If the shape or size of the 'sphere' of water is imperfect then this results in blurring of the image.
The light makes dents on the material of the retina (as described earlier) - on the rods (for black and white night vision) and the cones (for colour vision) and signals travel from them around the optic nerve. We have 3 cone types - each with its own distinct electric field and therefore sensitive to 3 different ranges of light wavelengths - and these result in signals which our visual cortex show us as red, green & blue and combinations thereof.  (Thus there is actually no red, green, nor blue light but there are ranges of wavelengths which our brain eventually interprets as colours.)
Important Point
From this discussion you should have learnt that it is the electric field part of  a photon which interacts with the electric fields of materials and the result is a slowing of the photon in its travel through the material. This is different to resistance as resistance would slow the photons more and more. Resistance certainly does occur in some materials - the ones termed opaque - the photons lose energy by other processes and a smaller number emerge than enter.
In very transparent materials when the light emerges from the material the compressive pressure of the material's electric field is no longer influencing the photon so it stretches out to its normal wavelength again.
One may ask whether the oscillating Magnetic Field component of the photon has any role in refraction. To date no-one is suggesting that.  The material referenced below solely speaks of the Electric Field component being involved,
David L Evans Ph D
21st September 2017
Publication
Evans D.L., Goode D.H.,A flexible automated data acquisition system for ophthalmic electrophysiology, Aust Phys Eng Sci in Med. used 15: 124–130,1992
Related material
MIT Lecture
https://ocw.mit.edu/courses/materials-science-and-engineering/3-024-electronic-optical-and-magnetic-properties-of-materials-spring-2013/lecture-notes/MIT3_024S13_2012lec22.pdf
Richard Feynman
http://www.feynmanlectures.caltech.edu/I_31.html
